I'm personally not having any issues with my iPhone 6 running iOS 9.3.2, with MS 2.20.30.
In previous car forums I participated in, many intermittent problems for iPhone and Android were resolved by completely un-pairing the phone from the vehicle, then re-pairing it. It's important to also then completely delete the phone on the vehicle if it's still there (but just not paired), and in reverse -- the vehicle on the phone. At that point, if I were you, I'd try rebooting my CID and my phone, then re-pair them together as if it were a new setup. If the situation then persists, I'd suggest keeping a log of when the failures occur and email Tesla Service with your VIN and those date/times so it can be investigated in your logs. Good luck.