If you had it plugged in for 15 hours and the batteries are at 11.8 they are bad and won't take a charge OR your converter is bad and not putting out a charge voltage.
To test converter with the RV plugged into shore power measure the voltage at the coach (house) batteries they should be 13+ volts and charging the batteries.
Unplug from 120V and measure they should be around 12.6 or above.
You might be able to save the batteries by charging with a regular auto battery charger.
Also check to make sure the converter circuit breaker has not tripped.
