Check that your refregerator door defrost switch is off. It is usually located right above the the molding on the door. It is used to keep condensation from forming on the door frame and will deplete the battery in short time if left on.
Actually it is not really a "defrost" swith but a switch to turn on a resistance heater that runs around the doors of the fridge to keep condensation from forming on the cold surface. Like any resistance heater, it draws a LOT of power. I believe the user manual says to use it only when running on shore power.
Barney