I was just playing a game where I had 20 seconds left and the opponent had 4 or so seconds left.  The opponent's clock ran out, then I got the message 'Server Disconnected'.  Then it said 'relogging in' and when it came back up, it said the opponent had won on time, when I didn;t even get another opportunity to move!

Here's the game (I was black):  http://www.chess.com/livechess/game.html?id=1326686

Yes, we apologize for the troubles in Live Chess. We are working very hard to resolved problems such as this.

lol, epic.