Just throwing in my experience regarding this issue.
I have been able to complete several 700-900 fights just fine. But the lagg in some of them was really really intense.
After I play about 5-6 fights without getting any bugs, the scrolls with the names of the different places in the world starts getting glued to my screen, and when this happen I basicly always get out of sync or fail to connect to other players. But if I restart the game it usually works again, at least for a bit