My iPhone 7+ with IOS 10.02 will not stream audio for more than a few seconds in a BMW 4 series with the latest multimedia software. I have researched the issue and others with BMWs and other makes seem to be experiencing the same-or similar streaming issues. Moreover, once the fault occurs the mobile telephone connection then becomes flakey as well. The only thing I can do is to disable the audio streaming option in order to have a phone that works in the car as a phone.
It has been stated by a few people that new releases of iPhones quite often have Bluetooth issues that are software driver related that seem to be fixed after a few updates. My old 6s+ with IOS 10.02 does not have this issue btw.
I guess my point is that it is pretty hard to believe that this software failure made it through the testing process. It creates a lot of angst among users and I am surprised it is not on page 1 of this forum!
If anyone has a magic fix I would love to hear about it.
I have the same exact issue as you, 7+ in my 2016 428xi. It only happens sometimes though, and once it starts working, it doesn't stop working until I shut down the whole system and the next time I get into the car.
I believe it has to do with iDrive 4.0 as that's what the 4-series runs and other BMW owners are saying their systems work fine.
I've found a workaround though, until then. Killing the music app a few times and toggling/untoggling random seems to get it to come around. Not sure which is doing it, but this has seemingly worked for me the last few times I've done it. Hope this helps.