Get a voltmeter..............
While plugged to shore power, you should be seeing ~13V at the battery.
If not then the converter is not working OR there is a wiring break between the converter and the battery OR there is a blown fuse in the panel;
While plugged into shore power - locate your converter and check the voltage on the out put side (should be > 12V); If you're not getting any power then the converter is fried OR you need to make sure the 120V fuse is working.
On some converters, there is a small LED which turns from green to red;
Check for any loose connections - remember you'll be around 120V - so be careful. On mine, the converter wire on the bus bar had worked loose, so you may want to check this.
IF you are getting 120V in and NOTHING out - then your converter is fried - Amazon is a good place for a replacement.
In the mean time, you can connect your battery charger to the batteries and keep it on all the time, this will keep the batteries topped up. Draining batteries, like you're doing now, will kill the batteries in no time.
Gerry