I would do the following to test it,
Take a wire from your battery, run it into the car, or perhaps, if you just want to leave the car parked, and run the wire from the battery to the PS along the outside for testing only, do that, run it to the ignition/acc wire of the M1. Put a switch in that line, so that you can turn it on and off, and just test the M1. Let it boot, let it shutdown. If your suspicion that it is the accessory wire is the culprit, this wire will prove or disprove it. If you still have about 80/20 success, then you know it is not the accessory wire.
Then, I would disconnect the switch wire that runs from the M1 to your MBs switch header, and install a seperate switch, like form a computer case, to it. Leave the M1 powerd by the accessory wire (or the one you previously ran to test it) and then push the button. Again, see if you still have 80/20 success rate. That will tall you if there is a problem in the connection between the M1 and the MB switch header.
Other then that, just confirm that all your connections are solid between the battery and the M1.