In a 2011, the house system should also maintain the chassis battery.
First test is to see if the boost switch is working.
While on shore power, push and hold the boost switch and see if the chassis battery volts come up to the house volts.
If the volts don't come up, that solenoid, which is the same one that maintains the house battery, is most likely bad. The internal contacts go bad and It doesn't pass current.
If the boost switch works, then you want to check the house battery voltage. It must be more then 13.4 volts while on shore power.
Do some testing and get back to us.