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I was playing a regular 3v3 (new beta map of shivering isles) with my two room-mates (same router). Everything was going fine when all of a sudden, the 3 of us got a "wait, attempting to reconnect" in the middle of our game. We did not lose our internet connection, as web browsers and skype worked perfectly well. The game kept stuck with the same message and we had to quit (getting a defeat in the process).
As soon as we quit the game, we noticed League of Legends was up and running, and we began a new game with no problem whatsoever.