Have a look in the Event Viewer
for any errors at the time of the shut-downs.
To open the Event Viewer go to Start
> Control Panel
> Administrative Tools
> Event Viewer
. Alternately, go to Start
and type in "eventvwr.msc" (without the quotes) and press Enter.
Check in all the categories (Application, Security, System and Internet Explorer).
If you find an error that occurred at the time right-click on it and select properties. Copy the information in the window and post it back here. This will help us diagnose your problem.How To Use the Event Viewer
Also, in Windows XP, the default setting is for the computer to reboot automatically when a fatal error occurs. An alternative is to turn off the automatic reboot feature so you can actually see the error code/STOP Message (which is also known as the Blue Screen Of Death (BSOD)).
To change the recovery settings and Disable Automatic Rebooting, right-click on My Computer and select Properties > Advanced tab. Under "Startup and Recovery", click on the "Settings" button and go to "System failure". Make sure that "Write an event to the system log" is checked and that "Automatically restart" is unchecked. Click "OK" and reboot for the changes to take effect.
This will not cure your problem but instead of crashing and restarting you will get a blue diagnostic screen with information displayed that will allow you to better trace your problem. Next time your computer crashes copy down the entire error message (including all the numbers) and post it back here.