The fridge is losing power (120v or 12v)
I kinda ruled out the 12V because it works on propane, unless it is happier with less voltage on propane, which is very possible if it causes the relay to drop out. But if that happens, I think it could then still be working, but on propane. IIRC, that relay will cause it to go to propane if it gets deactivated.
If there is a flakey contact on the relay for the AC mode only, that could explain it. Relay stays closed but with poor connection. That will be no AC as well as no propane operation when "auto" is selected.
And that will show up as no 120 AC to the heating element when it fails.
Intermittent AC to the refrigerator would cause it to switch to propane--ref would still be working, but it doesn't, if I understand Stevenattsu's messages correctly.
-Don- Borrego Springs, CA