InnaB, this is an issue with iPhone. This is just MY speculation, hope Apple will release a fix soon. You can also leave a feedback here
http://www.apple.com/feedback/iphone.html and PLEASE enter specific information of vehicle like Model, year and type of radio or Audio System your vehicle is equipped with when you fill out that feedback. I have encountered similar issues with other makes of cars too as I do a lot of testing of cars.There are some vehicles that work fine and then there are some that exhibit concerns like yours.
On a side note have you tried to RESET NETWORK settings and tried? Also unpair ALL BT sets, re-pair the iPhone to your vehicle and try it. Some instances I have encountered where the IiPhone was STILL paired to a HEADSET, it would NOT release it to work with another BT device. Some car audio systems have what's called an "Auto Pairing" which works awesome with iPhone, where you DONOT have to worry at all, start the vehicle, turn on audio system, iPhone auto pairs to that system. I donot know IF your vehicle is equipped with that design, check in the user manual of that system please.