I have a 2014 Winnebago sightseer. Chassis battery is only a year old and fluids are full. I have shore power(50amp) plugged in. However, if I leave unit unattended for a period of time(Still plugged...
We have the same model as yours, just called an Itasca. Ours and likely yours has the equivalent of a trickle start installed at the factory. It keeps both batteries topped up when plugged in. I don’t recall exactly what it is called, but it does the same thing. If yours does not do this maybe it is broke.