I'll deal with the simplest question first - Horrifying Visage is listed under the Ghost's Actions section, so it requires an action to use. While under the effects of Time Stop, this is impossible for them.
As for the question of multiple Ghosts using Horrifying Visage, the answer is contained in the rules quote you included:
If a target's saving throw is successful or the effect ends for it, the target is immune to this ghost's Horrifying Visage for the next 24 hours.
Immunity is only to a specific Ghost's Horrifying Visage, not to any Ghost's Horrifying Visage.
Ah yes, the effects of age, I could tell you a lot about that. But I’ll try to keep focused on in-game effects.
“I’ll regret this later”
Penalties to abilities that simply make the character weaker (like those found in older versions) are frustrating for a player, and they are bland, and don't really evoke the feel of old age. These rules simply never provided any fun, or much depth. It’s no wonder they didn't come forward to 5e.
Effects that limit the endurance a character has, that come into effect after some initial exertion, evoke the effects of age more poignantly, while letting the character still “relive past glories” in brief but glorious combat.
So very tired
The rules for exhaustion in the DMG can be utilized to simulate the fatigue of advanced age, and they come pre-play-balanced for you. A venerable character (depending on age, at the discretion of the DM) may gain a level of exhaustion from a single combat, and require a short or long rest to recover from it.
I just can’t seem to rest like I used to
Speaking of rest, an older character needs more. Simplest thing would be to double the amount of time needed to attain the benefits of the rest, but it doesn't add much color to the game, if the players are simply obliged to say “OK, then we rest for 16 hours.”
I find it’s better to “nerf” the effects of the rest, granting back fewer hit dice, hit points - or even fewer spell slots, if mental ability has been affected. That allows the oldster(s) to “try to keep up” while providing a nagging reminder they are really too old for this sort of thing.
(If you ever played 4E, this was like a non-heroic NPC taking a rest. Unlike the PC’s, the NPC would not wake up in the morning fully healed of all wounds.)
Another nice surprise
I would also suggest that these or any effects of old age should come as a surprise (especially for the prematurely aged). They always do.
My (game) experience with old age effects
I’ve used these rules for adjunct NPCs - I haven’t prematurely aged a PC. The players thought they were fair and interesting rules. It accentuated the power of the (young) PC’s, without making the NPC useless. The oldster slept/rested while the characters did ancillary stuff. It might be different for a PC. I suspect a player won't be overjoyed with having to “take it easy” but it's similar to other “curses.”
Since initially answering this, I spoke with one of my players about the age rules we used. She commented the rules made her feel protective of the NPC.
Best Answer
Yes, the ghost can continue to drain your life
Let's start with the spell mechanics (MM, 147):
The initial save is very clear in direction in that the target(s) must succeed a DC13 Wis save or be frightened for 1 minute. The next sentence is our key (emphasis mine):
The text does not state "If the first save fails" but simply "If the save fails". If you fail the first time, you repeat the save and are therefore under the same rules and risk for aging.
There are many spells/abilities that state "The first time", but Horrifying Visage is not one of them and therefore the risk of failures by 5 or more for aging remain.
And it's a cool effect!
Most importantly is the narrative behind the effect. You have encountered a horrifying creature and if you are completely enthralled by it from failures by 5 or more, the creature is still horrifying. Remaining under it's power after failing again by more than 5 forces you to keep aging because that's a reasonable and cool effect. Think of all the movies where a ghost ages someone to death; that's what is happening here.
Simply put, ghosts are horrifyingly scary
For those so inclined, Jeremy Crawford also agrees.
However, you do not HAVE to try and save again
The language clearly states (emphasis mine):
They do not have to repeat the saving throw and can instead simply remain Frightened and not risk further aging.
However - beware of metagaming! If your character wouldn't know to not try and shake off their fear, then they probably should still try.