Power drain?
I am wondering along the same lines as Dave R. After you are on shore power and the batteries are fully charged (I am assuming an on board battery charger keeps the charge at peak), disconnect the shore power and run whatever you normally would at anchor. I assume when you are "at anchor" you mean the engine is off and you are on batteries only. If you try this "at dock" test you eliminate the alternator charging system as culprit because you are not using it. If batteries die at the dock then either your batteries aren't really in as good a condition as you think OR you have a heavy current drain that is tapping them out. You could set up to test the amperage draw on the battery but I'm not sure what "normal" would be.
One thing to look for might be lights left on in enclosed spaces (engine compartment, glove box, etc.). I left my trunk light on in my car and it drained a brand new battery in a day. If it is a current drain it could be coming from just about anywhere in the system. Checking amperage through various wires could help narrow it down.
Good luck.
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