There's a balance between requiring money to upkeep the pet and the number of posts you make per day. If you need hundreds of posts just to keep the pet happy and on full health, there's a problem.
5% sounds fairly reasonable, although it might be interesting to link the percentage to how hungry the pet is - the better fed the pet is, the faster it heals. (In the range of 1% to 10%, perhaps?)
Actually, I think it should be a fixed number of hit points per day. Maybe 10.
The tougher creatures will take longer to heal, which makes it more likely that their owners will spend money on healing potions. That means they are spending less money on training and items, so the owners of the weaker creatures have a better chance of catching up.