I made progress with my Nexus 5X and 2016 VW GTI, yesterday. It is now connecting every time -- even when doing all of the things that previously made it fail to connect. This is good to see, after 10 weeks of wrestling with it.
It was kind of an unusual day, though. I went to the VW dealer and got my Infotainment software updated to 0613. (BTW, they would only do it, after I showed them the PDF of the service notice, from the link posted on this forum. My VW dealer claimed that there was no service notice, until I showed it to them.)
The unusual thing is that after the Infotainment SW update, it still took me at least 10 minutes and 8 or 9 different tries to re-connect Android Auto successfully. I did the usual things like re-booting the phone, clearing the Android Auto data, etc., and eventually it just worked from the usual brute force try-everything attempts.
Then, after all of the trouble, I called VW of America service (800-822-8987) to continue seeking help for the issue. While on hold, my Nexus 5X requested to update from Android 6.0 to Android 6.0.1, and I said "yes". Ever since then, it connects very easily.
So, I don't know if was fixed by the Infotainment SW update, or the Android Marshmallow 6.0.1 update. But I really believe it is connecting correctly now, without any special steps.
I happen to have an LG G4 (Android 5.1) available to me this weekend. I am going to do a factory reset on LG G4, and see if it shows the connection problem, or not, on my vehicle. I will post a brief description of what I find, in case it helps.
Good luck to all.