i was in the same boat as you just recently got the charge and bluetooth kept droppimg after a min or 2. same behavior, something not right with syncing the contacts. I sat in the car for a good hour syncing, dropping, re-adding, turned the car on and off, rebooted the phone a few times, evaluating my contacts list and getting ride of any special characters.
and finally it connected and stayed connected to my surprise!
I'm not exactly certain what finally fixed it or combo of events... but so far its been about a week and all is well.
I've heard about the contacts being an issue but I don't know if I'm fully convinced. anyway sorry I don't have a definitive solution but my advice, stick with it and keep on trying!! because it appears the car will eventually downloads all contacts as long as you keep reconnecting and once its finally done, everything is just fine.
2011 E90 M3
2004 996 GT3