This has just happened on my E60 and annoyingly also happened on my previous E39. I've just been into the dealer under warranty and it is caused apparently by a corroded connection to the aerial on the rear window. On my E39 I'd re-seated all the cables on the amp in the C-pillar but to no avail, not thinking about the actual screen connector. Presumably the dealer has cleaned the connector as all is ok now

Useful info for any fellow FM sufferers out there...

 

You definately have a problem. Your dealer should be able to fix that issue.
I only had this on a loaner and reported it, and they fixed it. So the dealers know what to do.

 

My FM signal fades in and out something awful - I've learned to live with it.