Despite it being a hardware problem as suspected would it be helpful to restore the system to a date just before this started occurring? If nothing else it might help rule out possibilities and support others.
I wish I could be of more help but I had a heck of a time with trying to allow my old vista system to hibernate upon command. So I had a similarly frustrating experience but under opposite end goals. It was a lot of reading among forums and how tos on Google that got it fixed for me.
if it was a PSU problem, then my PC would shutdown even during daytime when i use it cotinue for 5-6 hrs.
So i think their is a problem were it shuts down when it goes in idle mode(when i dont use it for 7-8 hrs)..i think
i will try to use XP for a day...hope for the best