It depends on the model and actual draw. Based on some numbers I have experienced with my 100 Watt MPT system and current draw for the fridge I found on line, here are my rough calculations.
Figuring 0.2A for the detectors and radio, that is 4.8A/hr per day.
Fridge draws 0.6A with flame and 0.2A without flame. Figuring flame will be on 50%, that is 0.6 * 12 + 0.2 * 12 = 7.2 + 2.4 = 9.6A/hr per day.
Total is only 14.4 A/hr per day.
A 55 watt panel should deliver at a minimum of 2A for 8 hrs and 0.5A for 4 hrs for a total of 18 A/hr per day.
Bottom line is the panel should keep the batteries topped off. With two batteries, you could handle 6 days without sun shine before the batteries will be pulled down to 50%. And for each day the sun is away, it will take about 3 days of charging to bring the batteries up.
I would recommend you invest in a battery monitor such as the trimetric so you will know the true status of the batteries. Otherwise, you will probably be running the generator to charge when you don't really need to be charging.
