Can confirm 8.1.1 did not fix the issue for me.
I have been able to reliably replicate the issue. Here's what I've found:
After a reboot, the phone continues to place nice when connected via USB to my 2013 Nissan Pathfinder SL. It does so over a number of days - in fact I've not seen it not work.
What does cause it to not work every time is playing any sort of video on my phone - YouTube (in the app), from a website, from Facebook - doesn't matter. As soon as I've played a video, the iPhone will no longer work via USB in the car.
So, for now, my workaround for this bug is to power cycle my phone any time I (or, more likely, my kids) have watched video on my phone. Annoying, but not impossible. It's definitely far, far from meeting my expectations of Apple.
BTW, for all of you that are wanting to jump ship to Android, you might confirm that your car supports it. Nissan does not support music from Android devices connected via USB very well - not at all in the Pathfinder. Yours might be a different situation based on your vehicle.