It sounds to me like it might have something to do with your machine's temperature. You can check to see what the temp is set to in the BIOS when your computer is booting up. You should be able to find out what yours is set at and change it to a higher setting. Before doing that, though, you might want to find out a "safe" temp to put it at.

Do you hear any sounds just before it reboots? I had an older computer that would give off an annoying buzzing sound and it would reboot. I had to go in and raise the temp limit.

It could also be that the power supply is getting too warm too fast. Being it's a built system, it may not have a strong enough power supply and you may need something stronger. I would check the temp first though.