Many RV propane 12 volt furnaces use a significant amount of 12 volt power to run the fan.
The needed 12 volt power must come from a battery, a converter/charger, or an inverter/charger.
A working charger is required to replace the power drawn from the battery. If the battery continues to discharge while connected to shore power, then the RV charger is not working as designed.
A fuse or circuit breaker may be tripped. They may be found on the charger itself or between the charger and the battery.
Some chargers can be switched "OFF".
RV chargers are powered by 120 volts through the main circuit breaker panel. Trip each circuit breaker "OFF" then back "ON". Sometimes they don't show that they are tripped.
Some RV chargers plug into a 120 volt outlet. Look to see it is properly connected.
Loose or corroded wire connections can prevent charging.
Post make and model number of charger for better advice.