Just had this thought:
If the feedback pins are not correctly wired to the Pi or they are flimsy, those GPIOs on the Pi side can float around randomly, causing the shutdown script to issue random restart/shutdowns, which could explain the behavior.
Double check those connections, maybe with the Pi off check for continuity.
Booting in console would allow you to see what triggers the reboot/shutdown, if they are caused by the SHUTDOWN pin or not.