Why is your battery so low? It should be around 13-14.5 v. You are shorting the life of your battery a lot by not keeping it charged up. If you are not camping and parking your unit, plug it in at home or disconnect the battery. You 'can' run almost everything in your unit with no battery and only use the convert, but it is not good on your converter. Also, if you are camping when it is colder and want to use the furnace, you must have a good battery to fire the furnace up. A low/ shorted out battery, even if it 'measures' 13.5 voltage, because the converter is 'charging' it, will still not have the 'reserve' power needed to fire up the furnace.
2013 Forest River Salem Hemisphere SBT312QBUD
2001 CrewCab F-250 7.3 PowerStroke Diesel
SuperChip, BTS transmission, 6.0 Trans Cooler