If you have one battery, assume 100 amp-hour, and you don't want to damage the bettery, you don't want to draw it down to less than 50% (50 AH) remaining charge. So, you have 50 Amp-Hours to "spend".
Of note - see normal appliance amp draws
for typical appliance draws.
From that post, refrig in LP mode - 1.5 to 2 amps (control circuitry monitoring the temp to decide when to light or extinguish the propane, I believe). Also, LP gas detector, 0.5 amps. On my Solera the LP gas detector is combined with the CO detector (1 amp) and controls a solenoid which turns on or off the propane. I believe the combined detector / solenoid draws 2 amps or so.
Refrig plus detectors, 3.5 +/- amps; for 24 hours, 84 Amp-Hours used - exceeds 50 Amp-Hour "no battery damage" limit in one day.
Conclusion - either decide to regularly re-charge the battery in some way or leave most everything (including the refrg, propane and the detector) off except for short periods when you want to use something specific.