I was at my dealer today, and saw a Dealer Communication System Message regarding this issue. BMW has acknowledged the problem but does not have a fix yet.
They said the affected vehicles are all BMW models produced before 09/2009 with option 655 (Sirius Satellite Radio). Dealerships have been instructed not to replace any parts or perform a repair attempt.
The issue is caused by Sirius/XM in combination with the SDARS-Exbox (SDARS receiver from Visteon). The SDARS-Exbox is the stand-alone satellite radio receiver (not integrated into the head unit).
Once again, BMW does not yet have a solution.