From: Computerpilot on 06/24/2002
Does the 'shutdown' include the whole process of your computer shutting down? For example, do you see the window that indicates 'Windows is Shutting Down'? If so, then you have some type of software that is shutting your computer down after a specified period of time.
How is your power settings? Do you have anything set up here for sleep mode? When you boot you computer back up, does it skip the whole login process and go right to windows?
Before I can determine if it is the power supply, I would be curious about all these questions first.
Why don't you check your power setting (control panel) and make sure that the computer is not set to shut off hard disks or go to 'sleep'. See if alleviates your problem.
If not, then make sure that your computer is really just turning off (much like pulling the plug from a desktop computer or turing the power supply switch to off). This would definitely indicate a BIOS or Power Supply issue. However...
...I am sure you have checked this out but are you on a power strip? If not, then I can see it possible that you are having brown-outs and your computer completely shuts down to avoid damage. Of course, a power strip is not your answer to this problem. You will need to get a UPS to fix this issue.
As you can see I have covered a lot of possiblities. There are more that I have not mentioned. This might get your brain thinking in the right direction.