Finally caught mine in the act of pausing the music uncommanded. I was sitting at home with my coffee reading in Safari on my iPhone 6S right in front of me while listening to an album previously downloaded from Apple Music. All the sudden the music paused. No more headphone icon at the top of the iPhone screen, and I think I remember seeing the Bluetooth icon grayed out or pulsing.
I looked down at my Apple Watch (Sport, 38mm, first generation) to see the red "Disconnected" icon at the top of the watch face. Huh! That's odd. I swiped up to get control center on the watch and noticed the Airplay button was highlighted in blue. Tapped it, and there my AirPods had jumped ship to my Watch! Ah ha!
After a few seconds, the watch reconnected to my iPhone, soon followed by the AirPods, but ultimately leaving my music paused. So... this is what's probably been happening, at least to me, and would explain both paused music, as well as phone calls randomly routing to the handset uncommanded.
What a weird bug! I hope it is software, and not hardware, so there's a chance to fix it. On other forums there seems to be a common thread of iPhone 6S and Apple Watch, which describes my situation.
Chatted with Apple Support his morning. They took all the information I could give them, gave me a case number, and asked that I do a factory reset of the iPhone and use it "out of the box clean" like that for a while to see if the problem continues.
Before I factory reset, I unpaired my Apple Watch and noticed an improvement. Virtually no dropouts, and had a 30 minute phone call with both AirPods, although the phone call had one bluetooth dropout where the AirPods spontaneously disconnected and reconnected. Haven't ruled out the possibility that the AirPods tried to connect to my MacBook Pro immediately downstairs.
I have to wonder if something specific about the iPhone 6S has a limitation with the radio chipset handling multiple devices (two AirPods, Apple Watch, multiple Tiles), plus LTE and WiFi. Add a little Handoff, and, well there's a lot going on, that's for sure, and might explain why the problems lessen when cellular is turned off, Apple Watch is unpaired, or only one AirPod is in use.... lightens the load on the radio. Just speculation.
Wiped phone clean, set up as a new phone, and now listening to Apple Music via AirPods. Not a single hiccup so far. Will slowly add things back.