you should report that.
Losing when your opponent runs out of time

What happened is that you were disconnected from the server. The timer on your computer was still going down, but no information from the server was getting to you. Thus, it looked as if your opponent wasn't doing anything when, in fact, they were waiting for you to move. Disconnects always count as a loss because if they counted as a draw, there's no way to say who disconnected accidentally and who did it on purpose to avoid losing.
This is why there's this announcement on the Live Chess homepage:
PLEASE READ! DO NOT USE LIVE CHESS unless you understand that it is still a work-in-progress. You MAY be disconnected randomly. You MAY experience lag. You WILL be disappointed if you expect anything else. For the BEST EXPERIENCE on Live Chess we recommend that you use Firefox 3, Safari 3, or Chrome. Internet Explorer browser does not perform well in Live Chess. Seriously, try !
We are working really hard on making Live Chess as fast, stable, and amazing as possible. In the mean time, please be patient - thanks!

What happened is that you were disconnected from the server. The timer on your computer was still going down, but no information from the server was getting to you. Thus, it looked as if your opponent wasn't doing anything when, in fact, they were waiting for you to move.
Ah, ok, fair enough. I hadn't had a disconnect before and assumed it would be more explicit if it did happen.
Thanks for the info!
Hey, I'm not fussed about losing some rating (I don't have much to lose), but thought I'd report a bug.
My opponent stopped playing at around the 9 minute mark, then the timer counted down. No response from my opponent (but I see some activity from my opponent in the general chat window)
After the timer finished, I waited a few minutes. I was a bit surprised to see no message about who won so I took a screenshot and shut the window. Surprise, surprise, In my live chess profile I apparently lost after "resigning".
See screenshot.
http://i225.photobucket.com/albums/dd8/trantor10/Lulu.jpg