I've put this thread up because I'd be very interested in whether this is a problem for other people. Is it? How do you rationalise this? What interesting houserules or alternative ways in handling it are there?
Much more than the problem of levelling up multiple times in the middle of an adventure, I have the problem of characters reaching the top level in too short time because of that.
For the first problem, it is enough for me to just think their next-level abilities were nearly ready but not quite, until at some point they managed to "unlocked" them. It may not feel right in all campaigns, but it's not that bad.
But the second problem really has no solution... unfortunately the game has only so many levels, so if your PCs start at 20 years old and before the end of the year they reach the last level of the game, then it is a huge blow to my suspension of disbelief, to think that all the rest of the world is so inept that it just watches them them gain 20 or 30 levels in a year, while NPCs, BBEG and monsters just stay about the same. You have the ol' Wizard who is 20th level when the PCs were 1st level, and they looked at him in awe... wow it must have taken all his life to get there... and then it invariably takes the PCs a year or two to catch him up
Many years ago I actually suggested in a thread on these forums that there could be (as a house rule) an age requirement for levels, but that would actually work against the players in many other campaigns.
So overall there's nothing you can do that can work for everyone. In my games, I usually don't get to run such long campaigns that I can plan long story arcs or adventures that spans months of gaming time, but OTOH this means I can afford not to worry much about this problem, since I end up typically running a series of short adventures with possibly a couple of background stories that develop slowly. This means downtime is easy to slip in.
In general, my absolute favourite adventures are not those combat-heavy parties with 20 fights in 24 hours, 7 days straight (in which case I'd just suggest to either (a) embrace playing it like a video game, this is not so far from what Gygax had in mind in the early years anyway, or (b) don't be afraid of dropping the XP down to 10%). My favourite is a LotR-type saga with many plots ongoing and laaaarge delays between "interesting days".