CJC, this was a pretty common situation on '03 - '05 Winnie coaches. Some people found that the Jensen, if that's yours, was not turned off (there was teeny button to press on the faceplate). Other people swore their radio got activated by spurious EMF (perhaps even a neighbor's garage door opener?). Some people replaced their radios altogether; others added their own mini on/off switch in the compartment. Try doing an advanced search (use the Find tab above) and keywords "Entertainment center" in the Winnebago Forum for say, the past 4 years...
(sorry I wan't much help for your resolving the problem).
If you're certain that only the outside radio is dragging down your batteries, you could pull the fuse for the radio, or switch the coach power off during storage.