Hi there,
Definitely Strange behavior forsure. Seem like a bad cap or something in the power-on segment. Improperly grounded outlet can cause ground loops and precharge a capacitor used to switch on the power ready signal. I have had this on a Touch sensitive device on a MMI unit in the fab when temporary power was setup for installation of a new machine. Intermittent IG was the culprit.
HTH
GL 
PJ 
Sounds like it is time for a UPS if its mission critical. 