My E39 also does this, very annoying. And as mine is a touring and the back is full a lot of the time on long hauls it always seems to happen just as I set out, I then have to either drive for hours with no CDs and the radio going out of tune every 20 minutes, or empty the boot to access the changer, and oftern I have engines and gear boxs etc in the back so not always an easy task.
I have just got a DVD/CD/MP3 unit with 2 screens for the head rests, I plan to use this with either an FM modulator or just wire it into the cassett internaly so it will work when cassett is selected. But I am struggling to find a location to mount it where I can access it from in the drivers seat!