It may be overheating.
Turn the computer off, unplug it and open the case.
Blow away any dust on the CPU's heat sink. It a rather large metallic piece with a fan. Any dust acts as a thermal isolant and prevent good air circulation.
Use canned compressed air. The air MUST be clean, dry and at a moderate ressure.
Also check the video card heat sink and fan. Dust it off if you think it may have accumulated some dust.
The power cord may be loose, or damaged.
Make sure it's intact and properly connected to the outlet and the computer's power supply.
Check the power management settings, it may be set to agressively.
Right-click the desktop and sellect "Properties"
"Screen saver" tab, "Power management" button.
Set "Monitor extinction" to a reasonable time, like 1 hour.
It may be set to as little as 1 minute.
Electro
March 2012
Automatic Answer
We may have found other answers which could help you.
howtomendit.com for free repair help, information and advice.
Try fixfault.com to fix desktop pcs.