Hi
The radio on this model is the main controller for all optical system elements(This controls all ecu units that are feed with optical light-audio etc) When you are resetting the battery the Optical system is automatically reset(most bus system reset takes place) and i suspect this is why the radio will work for a period of time.when the car is switched off the system will go into sleep mode and then when you unlock the car the optical system will re boot. if one of the ecu units does not start this will cause the system to shut down again and this will effect the audio system as this is a major component in the optical system.
This system is very complex and will need diagnosing professionally as the radio may not be the cause (radio for this model is very expensive)
Regards Steve
BMW Technician
city & guilds - Bmw Senior Technician