Much like with kids and animals, routine helps.

Accept that a certain amount of socializing will always happen at the beginning of the game, and allow it to happen.

before you start the session

• A half hour before you (as the GM) would like to start playing, put the food away and take out the books, dice, miniatures and other paraphernalia that you use.
• At the same time, ask your players to finish up any food (not snacks) that they are munching on.
• 15 minutes before you want to start ask your players to look over their character sheets and make sure that they are up-to-date.
• 10 minutes before you start, ask the smokers (if you have any) to go out for their smoke break so that they can get into character before going out for another.
• 5 minutes before you start, ask the players to think over what happened last session and get a brief summary of what happened, from the viewpoint of their PC.

start of the session

• Turn down the lights.
• Pick a player at random to summarize the last session for you. The choosing could be having the players roll a dice and highest/lowest roll does the summary. The recap does not need to be an intensive 5 minute treatise. Summarize it from the viewpoint of the overall story that has gone so far. Here, the recap does not need to be lengthy Shakespearean prose. Short and sweet will get the point across. (1)
• Start playing.

More abrupt techniques

• Simply pull out your stuff, and announce that it is time to play. Ask the player closest to the lights to turn them down, and away you go. Ignore people who are not participating in the game and reward those that do. Perhaps in-game rewards (XP, loot) or out-of-game rewards (get to choose munchies for the next session.)

Other useful techniques

• Ban use of tablets, smartphones and laptops from the table.
• Turn off wi-fi access or change the password while you are playing.
• Create a phone-zone where people can put their phones while playing, and they are only allowed to check them during pauses. (Note that as a husband and father, this may be more difficult to enforce.)

If you do this regularly, as well as making it clear to the players what you are doing, your players should start to accept that once the lights go down, chat time is over and play time has started. However, make sure, during the game, you allow for brief (10 minutes every 2 or 3 hours) breaks for people to unwind and loosen up. Turn the lights up at those points, and remember to turn them down when it is time to start up again.

(1) It could be as simple as "So, when we last saw our heroes, they just finished a grueling fight with Tucker's Kobolds. Gundar is bleeding from multiple wounds and is fatigued from raging, Gandalf is out of spells, and Friar Tuck is stuck in a web. What do you do" (stolen from the comment by Pulsehead, below.)

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.