I have an identical problem using my iphone 4s on IOS 6.1.3, i have even had My local Volkswagen dealer completely change my bluetooth module under my drivers seat.
Recently i spoke with Volkswagen Customer services regarding this issue, they say that the Iphone 4s, is apparently compatible with my bluetooth module (Part Number 5K0 035 730J),however when testing the two together they stated there were several issues including the problems we are experiencing.
I asked the advisor if Volkswagen were going to do anything to solve this issue, to which they stated in a very polite manner, no.
The issue lies with Apple, as to whether the next software update will solve any issues,personaly i don't think so.
i read on another forum that getting a Bluetooth module fitted to the car from a later model (for example 2013 onwards), which has the latest software. This appears to be a costly process, some in the region of £600, and still VW won't guarantee that this will work, and they will offer no warranty with this.
How can we solve this issue, not sure buying a iphone 5 will solve the issue, as the iphone 4s and iphone 5 have bluetooth 4, whereas the VW cars pre 2012 have bluetooth modules only capable of handling bluetooth 2.1, for which i belive the iphone 4 has.
Any body have any advice on this please???