If it only happens with streaming videos, maybe you could start by pinning down exactly what types of videos cause the problem. Do you run any special software to view the videos?
Does it happen if you download a large file that is not video?
Sounds like something is causing some type of conflict or memory problem on your system.
Check the event viewer to see if anything is showing as an error or warning around the time of the shutdowns.
Are you getting blue screens or is the thing just powering down?