Try replacing the 24-Pin ATX motherboard power cable ;)
Welcome at the VMware community forums.
As you mention the BIOS auto-reboot is only supposed to kick in after a power loss.
See if you can update the firmware/BIOS on your motherboard.
This is typically seen with a BIOS that isn't working as expected.
I've got a similar server where a scheduled restart ends up as a shutdown, of course it works fine if not booting vSphere, but that's just how it goes. Unfortunately in my case there are no more firmware updates for that server.
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