Neal,
I think you may have a problem with your battery isolator. If one or more of the diodes break down then you will fail to get charging current to the affected battery.
The symptoms we had in Alderney were as you would expect from this fault I think.
As Duncan surmises, a reading of voltage at the affected battery ( as opposed to the alternator side of the isolator ) will show that the voltage is not rising sufficiently when the engine is running.
So I would get a voltmeter and look at the voltage at the battery terminals.
- I think your GPS can effectively do this for you though ). With engine running I suspect it will not change / barely change
regards Paul