Awesome information. I have an hour commute, twice a day for work, and have been listening to podcasts everyday for the last 7 months on my commute without any problems. As of last week, my Note 5 started doing the same exact thing you're describing. It would maybe connect to the car for a few minutes, then it would all of a sudden turn off the Bluetooth all together. When I tired turning it back on, it would instantly shut itself off again. Clearing my cache and resetting would maybe make it work for a few more minutes, but then it would eventually do the same thing again. Same as you, I have had the Walgreens app on my phone for over a year and a half now.
After reading what you found, I went into the settings in the application manager, then into which apps can modify system settings (i.e. turn off Bluetooth). I was going to try and see if I could disable the app from being able to control the Bluetooth. But according to it, the Walgreens app was already set to 'OFF' for being allowed to modify system settings. So I went ahead and I uninstalled the Walgreens app. After doing so, my Bluetooth now works again like it's supposed to, and doesn't randomly shut itself off anymore. Thanks for sharing! I was really starting to get annoyed, cause I have very limited radio stations on my route.