I'm not an electronics experfect, but I would imagine there is a relay involved somewhere. The fact that the unit becomes unresponsive would seem to indicate logistically it has shut down. I assume this includes the fan, which is software controlled, as you say the unit heats up. Seems as if the hardware power down (last step) is not being performed or is failing, like a failed relay. Likely a mainboard faiult.
Since I run my units 24/7 this wouldn't be an issue for me
When you disconnect power, then reconnect it, does the unit power up or do you have to press the power switch?