I ran into this problem on the last computer I built.  It was used as the projection computer at church so it doesn't need to shut sown for any reason.  Has a high power UPS on it. First Sunday that the power flickered it rebooted.  Checked out the UPS and couldn't find anything wrong.  It too kept the monitor running. So called Cyberpower, the brand of UPS, and they said some of the newer better power supplies need a special UPS that cost more that double of the standard UPS.  Seems that the old UPS are too slow for that type of power supply.

You could unplug the UPS from the wall and the computer would still run, but a surge or blinking of the lights is what would send the computer into rebooting.  Decided I would try another brand of UPS so I bought an APC UPS of the same rating as the Cyberpower and have been waiting to see if it to lets the computer reboot.  Been waiting for a couple of months for a thunder storm during church to see how this one does.  If it works I'll post it back here.