Could be a temperature problem with the CPU or GPU. Download a temp measuring program, such as I8kfangui, and watch the temperatures while you watch the video. Videos are not too demanding on either processor, but will cause temp increases.

Even I have the same configuration and facing the same issue. I do not think its anything to do with temparature. The problem happens only on windows vista and not on the ubuntu which I have on another partition. Ubuntu works fine with videos hours long. It has to be some s/w (may be drivers) on windows which is causing this. I have installed the latest directx drivers from microsoft and looks like the problem has been resolved temporarily. Though its too early to confirm this as I installed this today (Feb 28 2010)

The problem occured again yeterday (01 Mar 2010) on windows vista while I was watcing an online video on firefox 3.5 I watched a downloaded video for a long time and there was no issue. Then I started watching an online video through firefox and the computer switched-off suddenly (as is the typical symptom with this issue).

Looks like my issue is resolved after following the steps in this:

http://forums.mozillazine.org/viewtopic.php?t=206213

The root cause as I could figure out was the temparature increase (heating up) of the laptop when watching videos online. Don't know why this happens. There is a lot of disk activity,laptop heats up and switches off automatically. Why this happens when watching videos on a browser, I am not sure. However I was able to resolve it after unstalling several video plugins I had on my system and installing the latest Adobe Flash Player and "Windows Medial plugin for Firefox" as mentioned in the above link