Sounds like the converter isn't working at all...it should provide 12V power when on shorepower and keep the battery fully charged. If it's not working, the battery is the only 12V power source.
To check if the converter is working, disconnect the battery leads and check the voltage across them with the camper plugged into 120V. If it's working, you should have about 13.5V.
Nights camped in 2013 - 55, 2014 - 105, 2015 - 63