Your rig is most likely on an E450 chassis.
The chassis battery quite often is not charged by the shore power cord. Some are and some are not.
There should be a battery control center somewhere. It should have a relay that will charge the house batteries from the engine.
Measure the voltage on the chassis battery with engine off. Then start the rig and measure the voltage with the engine running. Running it should be around 13.8 volts.
Some rigs have a switch to run the radio off the coach battery system. If you listening to the radio for some time at night it could have drained the chassis battery.
