You need a voltmeter.
To check the charging voltage under various conditions.
This sounds very much like your converter/charger has failed.
A more sophisticated one should solve the problem.....but if it is only off by a little bit.....you can certainly unplug the shore power cord and manually connect an automatic smart battery maintainer instead while it is in "storage".
You do NOT want anything that is labeled as a "trickle charger".
P.S. Although somewhat more expensive, AGM batteries are usually a better choice as they are maintenance free.
And finally, if you have a 12 V power socket available that is connected to the house batteries, I find that having a digital voltmeter plugged in there allows you to monitor the situation, more or less continuously.
'07 Damon Outlaw 3611
CanAm Spyder in the "trunk"