Are you 100% sure it is going into hibernate? If your not running a laptop, I would disable the hibernate function.
also, i would right click on "my computer" go to properties- go to the advanced tab - setup and recovery - click settings - check "write an event to the system log - check send and administrative alert - and UNCHECK automatically restart. If there is a system malfunction you should get a blue screen with a STOP: message. write this message in the post if it happens again. If your settings were already this way, double check monitor settings to verify wether or not it is the monitor or the computer itself. when it supposedly goes into hibernate, is there a message that specifically says "hibernate" and do you hear your computer shutdown?