I am assuming he figured he would lose, so instead of forfeiting, he literally just didn't do anything. He just went afk and after the timer would end for him without him doing anything, the next turn would come.
So, there needs to be like an afk check or something after a few moves. Spent 18 mins in a battle watching the other guy sit there and let the timer run out till it was my turn. Better than him forfeiting, yes, but far far more tedious.
Overall though, I love the whole system. Def a fan of pet battles. Sticking to leveling/acquiring the pets for the most part right now, so pvp pet battles only a few times. So, the above problem not too big right now, but definitely something blizzard should keep a look out for as more people get to that point.