Alright, some good news for those having the 'random' shutdown issue:
After digging through some code changes, I was able to reproduce this and realized that changes in how some status flags are set between the Power Manager and the CPU had changed between 0.3.1 and 0.3.2/0.4.0+.
If you hold the power button down for half a second or more, as you would to turn OFF the camera, the power manager will interpret this as a request to turn off after having entered the power ON state. Therefore, the camera boots, power management daemon starts before the rest of the UI, sees that a shutdown was requested, and then proceeds to turn the camera off.
The solution is to briefly press the power button to turn the camera on. Do not hold it down to start the camera, as anything > 500 mS will be interpreted as a command to turn off.
Please let me know if this mitigates the issues that everyone here has experienced. If so, I will add a delay sequence to the power manager so it correctly handles this button press.
Jeff, yes, the downgrade script is only to go from 0.3.2 to 0.3.1.