When regular trainers are rematched, how often to their Pokemons' levels increase?

Question

Sometimes Bulbapedia will say they use high-levelled Pokemon in rematches, but I challenge them over and over and their Pokemon don't level up. Note that I'm mostly interested in generations 3-5.

Comments

I've got your Gen 3 answer right here.  It isn't time based.  It's event based.  And on top of that, there's a level cap.  The level cap is different for every trainer, and often the different Pokemon among the same trainer.

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^^^
He's right, from my experience playing Diamond, Platinum and HeartgGold, their levels increase as you complete more in-game events. Mainly beating Gym Leaders. And there is a level cap.

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Gen3isbest, why didn't you just answer the question?

Answer 1

It's not time based, it's based on how many gym badges you have the next time that you battle them. Usually every other gym badge or so.

Some don't change though. Most do.

:)