Have you checked their site for software and bios upgrades for your model number ?
Remember that mother board manufacturers often send out fixes and patches for glitches that they discover later, after people use them etc. HP will have the bios updates for the mobo.
I think that Roy has a point with the bios, click around in it and see if there is anything that might be causing it to shut down at or about that time. Something is telling it to reboot or shutdown at that time.
“it immediately drops power” sounds like a scheduled shutdown to me. You indicate the computer works fine the rest of the time.