Based on the responses here, and based on my experience with this unit, this is what I think it happening:
When I'm out sailing, including overnight, the monitor works as it should.
Same when I have the shore power turned off while the boat sits in the slip.
If the battery becomes completely charged up, and I leave the shore power turned on, then for some reason the monitor does not register the fact that a charge is continually flowing into the battery (actually, batteries); it only registers the parasitic draw coming out.
This is not such a great problem, as long as I know it's happening, and as long as there is not a problem with the shore power. Anyway, in general unless the batteries are down, I don't leave the shore power (i.e. the AC main switch) turned on for days on end when I'm away from the boat.