My AirPods are now working great after having erased my iPhone 6S and set up as a new phone and avoided installing any apps or doing anything else beyond the basic requirements to get going. Able to listen to Apple Music and Podcasts (gotta love Daring Fireball) without the intermittent L/R channel hiccups or un-commanded pauses. Had several lengthy phone calls today including cellular T-Mobile LTE, WiFi, and FaceTime. In fact, I ran the AirPods down to very-low-battery-warning while on a call, popped the left one into the case, and continued the call on the right one, then switched to the left one after it had gained some charge. Not a single problem.
I've now paired my Apple Watch Sport (original 38mm). Still working. Connected AirPods to my MacBook Pro (early 2013 15") and watched a YouTube video. Paired to my Apple TV (4th gen) and watched another video. Worked great.
Finally was able to provoke bad behavior: on my Watch, swiped up for Control Center, tapped on the AirPlay icon. Tapped on AirPods. That worked. Switched to Apple Music app on my Watch. Tapped Play. Much heated discussion ensued between my iPhone and the Watch as to who gets to have the AirPods. Turns out they couldn't agree, so no music for me. Tried to switch back to iPhone, but AirPods wouldn't connect. Tried to make phone calls with AirPod's showing as the Audio device, but each time was dumped with "Call Failed." Replacing AirPods into their case for a few minutes seemed to reset things back to normal, and they are working again.
Received a voicemail from Apple Engineering in Austin, TX. Will try to get in contact with them and let them know my experiences and any logging they might want.
Aha... looks like I spoke too soon. AirPods just disconnected and reconnected on my current testing phone call. Hmm.