^^^^^x2
[Edit -- based on your Post #4 you have AGM batteries? If so ignore most comments below, but still test battery voltage. Solar charging may be limited, depending on what the dealer did]
Also . . . the batteries need to be fully charged and in good shape. If the dealer let them run down, they may be shot. Suggest unplugging from shore power and checking the water level in each battery cell. [using safety procedures described in your owner's manual -- gloves, safety goggles etc..] Use distilled water only to top off. After one hour without shore power, what does your monitor panel say the battery voltage is?
FYI, in addition to your owner's manual, this is a good source for basic info on RV battery practices:
http://www.batteriesnorthwest.com/batteryschool.cfm
If the batteries have been allowed to go under ~12.2 volts, their life expectancy has probably been affected IMO.
If your AS is still under warranty, the batteries are too probably. If problems persist, you might want to have the batteries checked by a dealer who carries your brand
You might also want to contact the dealer who left your Use/Store switch on Store. Why and for how long?
Presumably you have an adequate supply of propane?
Good luck,
Peter