My 2v2 partner and I have had our share of long Arena matches.
Back in the days when mana drain was a common tactic, we started taking screenshots of the time it took to win; 21min ended up being the highest, against a mirror match (pally/hunter).
However, this new record takes the cake: 45min, the current Arena match time limit.
Sure, we didn't win (in fact, both teams lose rating when a draw happens) and unfortunately I don't have any proof (it automatically ported us out almost immediately after the match came to a close)... but I still think it was a damn good effort.
I hope we get that team again in future - losing is one thing, a draw just makes me keen to try again, because I know we can beat them! :)