I don't disconnect when camping for a few reasons. If not hooked up, which is much of the time as we camp dry, than the fridge will need the battery to run.
If I'm hooked up to electrical (120Vac), than I trust that the converter is doing its job and keeping the batteries charged. If you believe your converter is faulty, there are ways to check it both at the converter and at the battery with a multimeter. Here are some manuals for various converters (since I don't know which one you own) Power and Electrical.
Basically, you are looking to check the DC voltage output. With the typical WFCO, this should be about 13.6Vdc +/- 0.2 unless you are in a bulk charge mode (14.4Vdc +/- 0.2).