advowson: Each training ground has a level cap, beyond which characters cannot train. Later training grounds have higher level caps, so as long as you progress through the game, the cap should not be a substantial burden. Also, as Waltorious noted, training ultimately becomes very expensive. If you want to push your level as high as possible (this is not needed), you will need a very rich party to pay for the training expenses.
Specifically, on Clouds alone (no travel to the Dark Side), the highest you can train to is level 20, and you won't be able to go past 15 until rather later.
On the Darkside, you can eventually train to level 200 (but will run out of money well before then), but it won't be until late in the game that you can go past level 50. The amount of money to get up to level 200 is significantly higher than the amount of money you can find in the game unless you abuse the bank by having a throwaway party work for decades (to accrue interest), then replace those characters with newly created young ones.
There actually is a serious issue with money in the late game; the game is very generous with XP, so you'll have enough to gain dozens of levels, but is extremely stingy with money, resulting in you not being able to afford all those levels you qualify for. It's rather annoying when the game keeps giving you millions of experience, but you can't use it because the game hasn't given you any money for a while, and even worse when a late-game dungeon requires you to either spend exorbitant amounts of money or be forced to take unreasonable amounts of damage. In fact, I consider this issue to be a rather significant design flaw in the game.
I also note that the XP needed per level stops increasing around level 13 or so, but the amount of gold needed per level continues to increase quadratically.
By the way, be aware that training takes quite a bit of in-game time; however, the amount of time it takes is independent of the number of levels you gain on a single trip to the training hall. Therefore, I recommend saving up enough XP to gain a bunch of levels before you go and train your characters all their levels at once.