WHY WON'T RADIO TURN OFF WHEN CAR IS OFF AND THERE IS NO KEY IN IGNITION

Hello, is this an original, factory Mazda audio unit? Some vehicles -- although I don't know if this vehicle applies -- will allow the audio to stay powered until the driver's door is opened. If this is "normal" for your vehicle, and the audio unit stays on even after the driver's door is opened, the driver's door switch may be faulty. This is the same switch that will turn the overhead light on when the door is opened also. Just a thought, but have a look in that area.

Key removed from vehicle - check it again in 15 minutes - is the radio still on?? Retained accessory power turns off after a predetermined time has passed - regardless. Is it possible it is just the battery failing perhaps.?