I found a solution which worked for me with this issue.
I have a 2013 Subaru Outback and I was having bluetooth pairing issues with my iPhone 6 Plus. I could pair but the next time I started the car, it would not repair automatically. The iOS 8.1 update did not fix the problem. I had performed the pairing using the Menu button on my audio console. Here's the solution I found.
1. I used the Menu button to delete the old pairing. I turned off the car.
2. I deleted the paired connection on my iPhone. I switched off Bluetooth and restarted both the car and the iPhone.
3. I turned on Bluetooth on the iPhone.
4. This time I used voice control on the Subaru instead of the Menu button. My voice commands were Bluetooth Setup-->Phone Setup-->Pair Phone.
5. I completed the pairing on the iPhone, entering the passkey. The pairing was successful.
6. I turned off the car. A few minutes later, I turned it on and - voila - the connection was reestablished. Over the last two days, the connection has been successfully reestablished maybe nine times.
I called my Subaru service rep just to give him this info in case anyone else was having the same problem. He said that generally speaking, it's a better idea on a Subaru to use voice commands to pair. Don't ask me why. Anyway, it works.
I hope this helps others with the same problem!