It sounds like a possible power supply issue?
Have you had any issues with the pc before this game?
My suggestion would be really stress the pc. ie get the cpu usage up at 100% (video encoding or decoding programs) and run your game at the highest possible settings.
Play the game now and see if the unit reboots under the 20 minutes specified.
If its power supply you really should see quite a few reboots under the 20 minutes though.
If you had access to a multimeter, you could check your supply rails whilst running the above tests.
Good luck
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