A few comments:
1. The OEM batteries that come with a new Airstream aren't the best and won't last very long. One battery lasted a year in our 2005, 19-foot Bambi, and the other one pooped out about six months later. We replaced both with Optima deep cycle (blue-top) batteries, which should last much longer. They have more capacity, hold a charge longer, and are slightly smaller than the batteries they replaced.
2. If I recall correctly, the propane sensor still blinks when the storage switch is turned off; and there appears to be other electronic devices that may also drain the batteries. We installed a separate, Perko (marine) battery isolator switch, commonly used on boats, that completely disconnects the batteries from the trailer. It is also nice, in case you have one weak battery and the other is still usable (assuming you discover this before the bad one discharges the other); because you can switch from using battery "A", "B", "BOTH", or "OFF". In the "OFF" position, both batteries are completely isolated from the entire trailer (and each other), and the only drain will be the internal resistance of each individual battery.
Since we installed the Optimas and the marine battery isolator switch, we have had absolutely no battery problems. We leave our Airstream connected to 110 AC all the time, so that we can use the lights, etc.. And, once or twice a month, and before we take it out, I turn the battery switch to "BOTH" overnight, to top off the charge.