Our 2004 Tioga had no provisions, like a BIRD device, to charge the chassis/starting battery. Your rig may not have the BIRD device either. You may be able to test whether the chassis battery is getting charged with a voltmeter.
With rig disconnected from "shore power", take a voltage reading at the battery terminals. Then, connect to shore power and take a voltage reading. Voltage should be around 13.6 volts or a little higher than previous reading with shore power connected if your rig has a BIRD device. I installed a Trik-L-Charge device and it works well. Installation was not really easy. I had to run a large guage wire from device to the chassis battery along the frame and up into the wheel well and to the battery with a 15 amp circuit breaker to protect from possible shorting. Could not find the easy relay connection described in instructions.
Whatever converter charger, etc., you have in your rig, periodically check electrolyte levels in all batteries and add distilled water as needed to keep electrolyte above the plates.