having difficulty

It has happened twice now. When I started uploading photos from the external drive, the computer completely shut down. It shuts down at other random times. One pattern I've noticed is talking on skype with a video causes it to shut down. Without a video doesn't seem to be a problem. It is not over-heating. What could be the problem? Does anyone know? Could it be because we keep our external drive plugged into our computer? Is that not a good idea? I'll try one more time...