If your radio is a Jensen JRV-212 or 215 it is normally connected to receive full-time power from the chassis battery but only to operate the clock memory - very minimum drain, like at the milliampere level. Switched power (RUN/STORE switch) from the coach (house) batteries operates the remaining functions.
The radio - if wired and operating normally - should not drain a healthy chassis battery. I've owned two coaches with Jensen radios wired this way and never had such a problem.
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