You could have a Converter / Charger issue if your not getting a full charge on shore power. I had an issue with my WFCO Converter before I upgraded it to a Progressive Dynamics unit shortly after buying my Magnitude. The fuses in the back of the Converter were very loose and not fit tight in their sockets. They would intermittently make contact not letting the house batteries charge properly on shore power.
If you run my tests, you can rule out your BIM as an issue.
You could as you indicated have a bad battery as well.
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