I just bought my third deep cycle marine battery in three years for my Rockwood Fifth Wheel. They keep going dead. I bring them indoors in winter and keep them connnected (plugged in) in the RV all ...
If you have a multimeter this is pretty easy to check. Measure the voltage at your batter while not plugged in. Next, plug it in and make sure the voltage goes up. If it doesn't, your converter is no working or is not connected properly.