That's got to be annoying! My computer gets way too warm after about two hours of playing videos, so I usually don't watch more than that. But shutting off completely is just weird. Did you ever find what the exact problem is?
It doesn't completely shut off...but the video loses so many frames that it's unwatchable, and it goes out of sync with the sound.
I don't know that there's a specific reason. But it's beyond aggravating.
If I wasn't so broke...it'd be something of a motivator to get a new machine one of these days. This one isn't ancient, but it's not new anymore, either, by any means.