1. Leveling up
2. Maximum amount of APs you can save and transfer from turn to turn is capped to a certain number, depending on your... constitution or a score between few main attributes. You can see this either in the character screen somewhere... by mousing over these various stats, if i remember correctly.
Cant remember the exact one but it should be one of the AP related ones. Probably in the section of character screen that shows your overall scores for health, damage, offense rate, APs and others.