What is the battery voltage when you go to bed?
Are you boondocking? The furnace is the largest consumer of propane and battery juice in the camper. At voltages less than 11.5 volts, there may not be enough juice to reliably open the gas solenoid. This equates to a battery voltage monitor indication of "L" or "LOW." It will actually be nearly DEAD when the "F" light (FAIR) goes out.
Boondockers in cold weather almost always have 2 batteries for this reason (and many others).
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW