The Dometic refrigerator in our 04 Roadtrek uses no electric power when on propane. I know some of the newer Dometics use 12 volt electric power even when on propane. Even so, I would think the draw would be pretty low. Also, the engine alternator should be able to keep up with all but the heaviest electrical draw. Are you sure the battery is in good shape; taking and holding a charge reliably?