The primary function of the store switch is to simulate disconnecting the battery from the system, eliminating the need to physically do this at the battery itself. That said, there are a couple of items that are still connected, the Propane detector being the most prominent, most likely because of some safety code. The radio isn’t one of those items.
To keep a constant
12v, Airstream would have to run a dedicated wire along with a fuse at the power source to protect the wire. You could do this, although running a hidden wire could be extremely difficult. A more radical approach would be to create a rechargeable battery backup for the radio isolated from the trailers
12v circuits. Or replace the radio with one that has a backup built in. Given that cars rarely have their power disconnected, most radios don’t have this feature, although a prior poster indicted theirs did.
If this is super annoying, you can also take another approach and look at why you disconnect so often and what you can do to eliminate that need. As the old joke goes, “Doc, it hurts when I do this”, “Well, don’t do that”
Greg