So, how do I get out of the vicious circle?

Stop doing the thing that's causing it. You diagnosed this yourself:

It's probably the worst issue I have as a Game Master, I think of a Game, I write a campaign plot for it, End, Beggining and Middle, get Hyped, Hype my players, and after 2 months I want the story to end, and it's usually too late to make changes to the GMing style I use by then, so I just dissapear some weeks and invent I have stuff to do, cancell the game, and run another one.

1. You find a game, like D&D 4e, and a beginning-to-end plot for it.
2. You play it for a couple of months.
3. You cease to be interested.
4. You find a new and shiny thing to be excited about—which is fine, there's lots of new and shiny things it's pretty reasonable to be excited about. This might be another game like D&D 5e, or a new kind of story.
5. You lie to your players (that is what you're doing) and stop the current game.
6. Return to step #1, and repeat.

It's absolutely no surprise one of your players seems concerned: she is concerned, and has good reason to be. It sounds like you've done this at least a couple of times, and your players probably realise by now what's going on—including that you're not being honest with them. You are clearly not having trouble running games in general, though you have stuff to do sometimes. That's fine! Strangely enough, though, whenever you're available to GM again, you aren't interested in continuing the previous thing.

It doesn't take much for someone to see through to what's really going on. They have probably recognised you're just becoming disinterested in stories. Now it has reached the point where you're beginning to hear concerns about it.

That said, it takes some courage to confront this stuff and ask people about it, so kudos to you for having that courage and doing that.

So, how do you break your cycle and stick with one game and enjoy it?

There are always going to be new and shiny things. You are totally justified in getting excited about them. The problem is not that there are new and shiny things, it's that you're letting yourself cancel your games all the time prematurely.

Cycles get broken by recognising the steps, and doing something that interrupts the normal progression through them. Change a step or a critical detail in it, or do something that blows everything apart.

There's a few options to break this problem:

1. Run shorter campaigns

Run shorter stories that only last a few weeks. Have player buy-in that they are going to be short campaigns and that the story will not necessarily continue. (Of course, nothing's stopping you from continuing the story a few months later.)

This lets you switch every now and then harmlessly.

2. Keep it fun for yourself too: don't plan the middle and end.

You probably bore yourself out during your games because you already know the entire story. For the players it's all new and exciting. You already had all that excitement while you were writing the story, and now you're going through the motions waiting for all the stuff you planned to happen, which is boring.

I suggest you stop writing stories that have a beginning, middle and end. Design stories that have a beginning, and then put your players in that beginning, and discover the story with them. This means you're having excitement as well as your players lead you in unexpected directions, and your planning & development fun is spread out over the full length of the game.

BESW and I run games like this: generally, at the beginning, there is a situation at a tipping point where the status quo is about to be disrupted (e.g. two factions are reaching the peak of tension and about to break out into war, and a third faction is rising in the shadows), and the players are positioned as the perfect X factor, with the power and autonomy to influence how events pan out. And then we let them pan out, and give the players and their characters that autonomy. We loosely plan only a session in advance, and we have people with their own individual goals (and not scripts) who we can improvise easily enough, because the players will probably surprise us by doing nothing we expect, and ruin any plans we might have in the process. And then we have fun discovering the story with them.

Try that out.

3. Have someone else GM

Really. If you think your GMing style is a major problem, have someone else be the GM who is willing to run this in a way you're not. It's pretty simple. Then join in and play with your group.

Also an option: open up and be honest with your players.

Tell them what's going on. Tell them you're having trouble staying interested in the games you're running. Tell them you are getting excited about new stuff. Tell them you'd like to be able to run these stories through to completion, and that you're having difficulty doing so. Admit to them you were lying about having things to do because you weren't sure how better to handle the situation.

This might take a little bit of courage to own up to, but it's going to have a lot of benefit.

This will put this issue out in the open, and open it up for people to talk about it. It will likely only confirm what they already suspect but do not feel they can talk about.

Your players will then actually be able to talk about this openly with you, without so much tension and awkwardness being there. Some of them, possibly the girl who was concerned about the current story, will be able to talk to you about possibilities around revisiting that previous story or character she really liked and wants to see more of.

Some of them may be upset. Some of this upset will be upset they already have there because you keep cancelling games, but have not been able to express because this issue has not been open. Be prepared for that, accept it, and be compassionate toward them. If they're your friends, they're generally going to be on your side.

It will also relieve you of the heavy burden of having to deal with all of this all on your own and having to keep it all secret and everything. It will let you actually talk to them about it, get their help and support, and as a group you'll be able to work out how to go ahead from here, among the options in other answers and this one.

You're only human, so have some compassion for yourself, and let the people who care about you help you through this.

This is a known tendency of 3.5...

As KRyan correctly points out in his answer, to a certain extent this is just the way 3.5 is. There are many options available to players (Save-or-Die/Save-or-Lose/No-Save-Just-Lose spells, ridiculous amounts of damage like you've seen with your Barbarian PC, etc.) that instantly remove enemies from an encounter.

There aren't a whole lot of options for "soft" defense - there are immunities, there are things like immediate actions that protect you from a given attack, but there aren't a lot of good ways available to players to reduce the impact of incoming attacks (many of the best spells are strictly all-or-nothing; Damage Reduction doesn't scale well enough to be an effective protection, etc.).

Put those two things together, and you get what's often called rocket tag - the two sides trade blows that will end the fight if they land, they do their best to prevent enemy blows from landing, and whoever [fails a save/isn't immune to something/takes a full attack/etc.] first loses.

...but it can be mitigated somewhat, by picking options for your enemies that aren't available/optimal for PCs.

The best way I've found to mitigate this issue is to make enemies who are better at taking/preventing damage and other fight-enders than they are at ending fights. This requires building your enemies much differently than you would if you were building them to be effective PCs. Some tips for this approach:

• Make your enemies immune or highly resistant to the standard encounter-enders. Sufficiently high saves prevent save-or-lose spells from being reliable, but if you want to be sure to prevent rocket tag, you may also want to layer on effects like Death Ward, Freedom of Movement, etc.
• Give your enemies lots of HP. As KRyan says, this isn't enough on its own (it just incentivizes your players to use attacks that don't deal HP damage), but combined with defenses against non-damage attacks, it can result in more uptime in fights.
• Give your enemies immediate action defenses, Contingencies, etc. One-shotting an enemy isn't a very satisfying fight outcome. Using your first one-shot move, having it countered by something like Celerity (SpC), then having your party member use a second powerful attack that lands because you've already burned through the enemy's defenses? Feels more like you've accomplished something, and less like you've trivialized the encounter.
• Have your enemies use lots of attacks that work over time, but not very many encounter-enders. Save-or-suck spells like Bestow Curse, damage-over-time effects like Power Word: Pain (RotD) or Freezing Fog (SpC), battlefield control like Web, grappling opponents (if your PCs aren't immune)...these are all strong options that make the PCs feel like Bad Stuff™ is happening to them, without instantly knocking them out of the encounter entirely.
• Use the terrain to make it harder for your PCs to land encounter-enders. If a competently built pouncing Barbarian lands a full attack on pretty much anything, that thing is going to die. So place obstacles that make it hard for the Barbarian to charge, use enemies that fly if your PCs have trouble with that, use incorporeal enemies that move in and out of walls to force your PCs to use readied action attacks, etc.

But isn't this unfair to PCs who specialize in the options I'm hard-countering?

If you just drop it on your PCs with no warning in a game where they've gotten used to normal enemies, yes.

The reason 3.5 has a tendency toward rocket tag is that PCs (and enemies who work roughly like PCs) are much more effective if they build toward offense than defense. In order to counter this tendency, you have to use enemies who don't work like PCs - enemies who have strong defenses that aren't available to PCs, but at the same time don't use some of the most effective offensive options that PCs do.

This may interfere with your players' enjoyment of the game:

• If they expect enemies to be playing by essentially the same rules they are, then the fact that those enemies are immune to lots of their attacks may strike them as unfair - "If that monster's magically immune this stuff, how come I can't be?" or "I spent all these character resources investing in high save DCs for my spells, and now you're telling me the big bad is immune to everything?"
• ...and the fact that their allegedly powerful enemies don't just kill them with encounter-ending spells that they aren't immune to might ruin their suspension of disbelief - "The evil wizard forced me to tromp through his tower full of Freezing Fog fighting skeletons before getting to him. And it was a cool fight, but Freezing Fog is a 6th level spell. If he could cast 6th level spells, why didn't he just nail me with Irresistable Dance on the first round and call it a day?"

But at the same time, you're the DM. Your enemies don't have to be built using the same toolkit that's available to the players, and there's no rule that says they have to have the same capabilities, or be vulnerable to the same forms of attack.

So, talk to your players! See which is more important to an enjoyable gaming experience for your group: enemies who play by the rules, or fights that last longer than three rounds? If you have players who feel they would be unfairly affected by these sorts of changes (e.g., a Beguiler who will be useless if all important enemies are immune to [mind-affecting] stuff), see if they would be okay with being allowed to rebuild their characters to take them into account, or if they prefer the game in its current form.

Then decide how much of this encounter redesign you want to do, with your players' needs and preferences in mind.

What can your players do?

Finally, to address your last question about what your players can do to mitigate this: nothing, unless you change how their enemies work.

The reason 3.5 tends toward rocket tag is that offensive options are stronger than defensive options in the default game. Thus, the best way for PCs to keep themselves alive is usually to take enemies out of the encounter as quickly as possible. From your question, it sounds like your players are already doing this.

If you want to make defensive options viable for them, you have to change the challenges they face - make it so that taking enemies out of the fight quickly is impossible, and then it's no longer the best way to stay alive. Make it so that enemies use damage-over-time effects or debuffs instead of deadly finishing moves, and healing/defensive buffs (besides the ones that provide immunity to encounter-enders) become stronger.

Your players are already doing the right stuff to stay alive in the kind of game they're in. If you want them to behave differently, you have to change their incentives.