[Festus2]

I may have missed it but if you are plugged in to shore power, then your converter, if it is functioning properly, should be charging your battery. There are, as you pointed out, various parasitic drains on your battery - the stereo lights and some of the detectors, which will, over time, eventually drain your battery if it isn't being charged up from time-to-time.
If your battery is "good" it should not run down in a day even with these parasitic draws. There must be some other drain that is causing your battery to become run down or your battery is not in a condition to hold a charge for a reasonable length of time.

You might consider installing a battery cut off switch which would help prevent some of these issues from occurring and check your battery with a hydrometer to see if each cell's SG is ok. It shouldn't be necessary to pull your battery out after each use --- just disconnect one of the cables (+ or -).