Ours is a dual carbon monoxide and propane gas detector, and only the CO lights were going on. Also, it is wired into the main battery for the trailer instead of having its own separate battery like the smoke detector.
It does sound like you have an issue. Not sure what. A volt meter is probably in order. Check to see what voltage you currently have on the battery. Then plug in and check to see that it is charging. Even with the fridge drawing power while on propane, it shouldn't drain the battery that fast. Maybe it is not a deep cycle battery?
We had that happen once. The furnace was running and the kids were running in and out of the camper. With the furnace exhaust port right next to the door on our 30CKthe wind was helping some furnace exhaust in the door every time it opened kicking off the CO2 detector. Our detector sets at the floor level right inside the door. If your fridge was running off of propane maybe some exhaust was making it's way in the door?
We just had that happen last night. Furnace was NOT on, refrigerator was on electric. the only thing we had going was the fireplace. We reluctantly called the Fire Dept to come and check it and they brought their Carbon Monoxide detector and there was none. We pulled the cover from the lower front of the fridge where the unit is located and removed and put back the fuse that was down there. That seemed to solve the problem for now. We'll see. If it happens again we'll be calling our friendly Cruiser dealer and having the unit replaced.