Potions VS Monster Enhancers

[Gidoza]

Monster Enhancers say plainly on the card that they boost a particular monster's combat strength, whereas Potions/Usable Once Only Treasure cards say "+X to either side."

My question is: Do the Potions/UOO cards affect only a particular monster, only simply the monster side, which is to say that no matter how many monsters enter or leave combat, those Potions' bonuses are in play until the combat is done?

Incidentally, if I want to be really stupid about it and the above is true, could all monsters be removed from the combat and the Potions' bonuses still linger such that a Munchkin has no monsters to fight and lose the combat anyways?