Your engine's alternator is properly charging house battery while driving.
Your converter cabling to the house battery may not be making good connections or the house battery disconnect switch/relay may not be working properly,
(you should hear a snap or clunk when you turn the house battery disconnect switch on and off coming from the battery compartment. If those things are OK, the converter's charging circuit may not be working. I just replaced an OEM converter that was boiling out batteries with a modern PD 9245 converter that works very well.
Replacing the converter is very simple
All batteries need periodic checking of electrolyte levels and adding distilled water when needed to keep the plates covered.
http://www.progressivedyn.com/prod_details/rv_conv/rv_converter_pd9245c_2.html