First guess might be that the coach batteries or connections to them are bad!
There are two 12Volt systems, one for the normal truck things like starting, horn, and lights and then the coach system for the things required for an RV.
What you describe sounds like this!
Coach battery not letting the steps work, but the chassis battery starts the RV engine. When that engine is running the engine alternator and chassis battery get connected to the coach system.
That connection and running for a bit gets just a bit of charge in the coach battery and coach things work for a short time.
But when the engine was stopped the two systems disconnect from each other and after a bit that little bit of power in the coach batteries is gone and things stop working again!
We can do a better job of looking for problems if you tell us the year, model and floor plan of the RV you have as that lets us look at drawings in many cases.
Can you pick out which RV?
https://www.winnebago.com/Files/File...ram/Wiring.htm
Then if you have a meter to check some voltages, it will speed thing along with less guessing involved!
A basic thing to check is that the coach battery disconnect switch is turned on but I suspect that will be true if things worked while driving!
Good luck on the bug hunt and let us know what might help from there!
Getting the battery operations in mind is one of the bigger things to figure on RV and we have all been there at times!