Did a test yesterday while sitting at a cafe: phone in airplane mode, Bluetooth enabled. Repeatedly played various saved voicemails in the Phone app. AirPods would randomly disconnect from the phone just like my experience trying to use the on phone calls. Sometimes there is the disconnect / connect sound, but more often no indication they've dropped.
Also on my daily 3 mile walk, AirPods would randomly disconnect causing Podcast app to pause and change volume level to that last used on phone. Who's is different behavior than I get when removing one AirPod (volume stays set).
All I can figure out now is it's either my phone or the AirPods, but given I don't have problems with other Bluetooth audio devices... Going to try to get a replacement set of AirPods, because I love everything else about them: fit, sound, compactness, etc.
Starting to wonder if mine have a poor connection inside or a marginal component.