How Long Will My RV Battery Provide Power?
On our first RV trip in our fifth wheel we stayed overnight at a state campground with no hook-ups. Our two batteries lasted all night... even with the furnace keeping us nice and warm. But when Fran started breakfast and wanted to use the microwave there wasn't enough power left in the batteries to start the generator! (I connected the umbilical cord to the truck and used the truck battery to start the RV generator)
How long your RV battery will sustain you depends on how much energy is stored in the batteries and how well you conserve it. There is no definitive answer but I'll try to give you some perspective.
Some RVers claim one 12v battery will last them about 48 hours if they don't run the furnace, carefully use the lights and water pump and otherwise conserve power. Some even use candles or go to bed early.
Fran and I are good for a weekend in our fifth wheel which has two golf cart batteries with modest conservation. Remember, a golf car battery is six volts so you will need at least two.
One last thing, I'm not sure all monitor panels work the same but when I'm hooked up to shore-power the battery indicator reads the voltage from the power converter. I learned this the hard way when I disconnected from 120v power after a long stay to find my RV batteries boiled dry and dead!
To get a true reading of my battery condition the converter has to be turned off. You may want to check how yours works.
You should check the water level in your batteries at least once a month. More often if you are cycling the RV batteries or the ambient temperature is high... like summer in Arizona.
You may also want to read: What's draining my RV battery even when everything is off?