If you faint during a fort battle:
you will be transferred to the hotel in your town (if you don't belong to a town, you will stay at the fort)
you will lose any cash that wasn't deposited in the town bank
you will lose all your Energy points
you won't receive any money as a battle reward
If you survive the fort battle:
you will remain in the fort
your life points will drop to the value they were at the end of the battle