So I thought the health of opponents increase for each pet depending on how many times that pet has beaten the opponent, but when I was doing a battle quest with a pet who had beaten the same opponent (rock, paper and scissors) its health was back to the default. Is it random or just when doing quests or what?

During battle quests, all opponents are at base stats. When you just challenge them normally, that's when they get the extra stats.

Thought it might be...thanks!