I was having the same problem but with iPhone 5. I found out that my Microsoft Outlook and Lync along with Exchange were duplicating contacts. This made the car go crazy trying to transfer contacts to the car, and this made the system decide to drop bluetooth.
First I decided to change setting on the iPhone to not transfer contacts. This fixed the problem.
But since I did want my contacts in the car I deleted all duplicated contacts manually on the iPhone and this fixed the problem definitely.