In my opinion heroes should start a battle at the health of their previous battle but if there is a healer on their team they should be able to increase their health if they had any energy/mana carried over from their previous battle.
And the other heroes should be able to attack them.
I hate the fact that in this game you make all that progress and it resets after every battle, there should actually be a reason it resets but I don’t think there is one.