I had a similar problem to you, radio sound (and CD) would stop after 40 seconds. If I stopped the car and turned the ignition off it would all work again, sometimes for 40 seconds only, other times it would work all the time.

I'll try to explain what happened, but it’s really stretching my knowledge of how the car works!
The DSP provides all amplification to the car – so the Radio feeds the DSP witch then amplifies the sound to the speakers.
All of these components are controlled by the i-bus, this provides communication between all devices and controls how the devices operate – for every button press etc etc.
As part of this communication process, every device is polled to make sure its alive and that it can be communicated with.
In my situation, it appeared that the DSP was not responding to any i-bus communication, if it fails to reply to the polling, the car thinks it is not there.
If the car thinks the DSP is “not there” it will grey out the display on the sat screen and, if the DSP thinks its not connected as it hasn’t received any polling requests from the i-bus it shuts itself down – end result no amplification and no audio. (This may not be exactly how the i-bus works, but its my understanding - I'm sure someone will put me straight!)

Its worth checking all the connections to the DSP amplifier and maybe reseating them – that may be sufficient to get it back up and running. Also check that none of the cables are shorting to ground as this could stop i-bus communication.
I reseated my connections to the DSP and I’ve not had a problem for a while now.

__________________
'02 X5 3.0d, Auto, Topaz Blue