What kind of fridge? What size battery bank?
An RV absorption fridge on propane will easily get through a night unless your battery is in dire need of replacement (and probably it would even then). Typically you could go a couple days or more, sometimes a good bit more, with a single battery and propane, though RVs do vary in their electric requirements some, and things other than the fridge can eat away at the capacity here (things like the LP and CO detectors).
A residential fridge, as a very very rough rule of thumb, needs to have a couple of batteries per day of dry operation, assuming no recharging from e.g. solar is going on.