Well Sir,
You've been given some good info. Since I don't know your model of coach you have, based on what you're saying, it sounds like a gas coach. If so, most of those are equipped with what's called a "Converter". Now, some of them are also, "Converter/Chargers". Basics are: A Converter changes 110VAC to 12VDC and, a Converter/Charger also charges mainly the "COACH" battery(ies).
So, the first thing I'd do is, dig around in your paperwork or, manuals and find out what exactly you have. If it is a Converter/Charger, then you'll have to determine if it's doing its job of CHARGING the house batteries while being plugged into shore power. The simplest way to do that is, using a VOLT/OHM meter, check your house battery(ies) when NOT plugged into shore power or, having the main engine running.
Record the voltage. Then, plug the coach into shore power and, check the coach/house battery(ies) again. If you find a higher voltage than before, it would seem the Converter/Charger is doing its job. But, if you find no difference in voltage at the house battery(ies) after plugging in and, you're CERTAIN that you have a Converter/Charger, then something's amiss in that circuit.
I don't know those very well so, it may be something as simple as a fuse on or in, that Converter/charger. Now of course, as has been stated, always make sure that your house battery(ies) are in proper condition and, plenty of water and, have good, clean and tight connections and, the cables are in great shape.
And, along with that is making sure that your ground cables and ends where they attach to the frame etc. are clean and tight. So, those are a few points to start with. Good luck and, do post back if you find the problem(s) so that others may learn.
Scott
Scott and Karla SDFD RETIRED2004 Itasca Horizon, 36GD Slate Blue 330 CAT
2011 GMC Sierra 1500 Ext Cab 4x4 Toad
2008 Caliente Red LVL II GL 1800 Goldwing KI60ND