I’m using a inverter+itps and a amd board, but i very occasionally get the same problem. I found out that when power its shut down ( in my case, when the itps cuts the power to the relay that is between the battery and the inverter). The itps feeds a very small pulse to the output that is connected to the pc power switch. This sometimes is enough to make the pc start, and since its power is cut immediately after, when it boots again it no long resumes from hibernation.
Don’t know if it's your case, but I thought you might want to explore the possibility.