[rohrmann]

Sounds like your converter is not producing 12 VDC. That would cause your batteries to be drained below a voltage that would enable your fridge to operate on gas, as 12 VDC is required for the fridge start up and run on gas. You might get lucky and find the 120 volt breaker that powers the converter is tripped and are able to reset it, and that makes the converter work again, but if that doesn't happen, more testing is needed to confirm a failed converter.