My trailer is at the dealers at the moment because it is doing just what you describe. There could be any of a number of causes; some are:
- Low gas pressure
- Clogged up burner
- Gas thermostat not working
- High flame solenoid not working
- Circuit board problem
Most models have a separate thermostat for gas and electric operation.
As for the 12v failure; sounds like a burned out 12v heater element. They are relatively easy to remove and replace. In 12v operation, there are no thermostats or circuitry involved. The 12v is simply turned on and left on since it is not powerful enough to cause freezing problems. That is why the element is the most suspect.
In my case, it appears to be the citrcuit board staying in low-flame mode since AC operation cools well enough to freeze food in the refrigerator section at the coldest setting.