Breaking out of a neverending battle without leaving the match

Recently, I was in the Battle Factory in Pokemon Emerald and was put up against a Pokemon with maxed out defense stats. I was using Latias, and had the opponent's attack at the minimum. Unfortunately, all my other Pokemon had fainted and we were both low on PP. Normally this wouldn't be a problem, but we were both holding Leftovers. After about 40 minutes of struggling, I did the math to see the probability of one of us getting enough critical hits in a row to end the battle, and promptly decided it was best to just forfeit and end my 70-something winning streak.

What can I do in the future to get out of such endless battles without leaving the match?