some more data points:
-Bluebird X's, for me, have had the same issue with not only my iphone 6, but my previous Note 2, Note 3 and S5. If there were any other bluetooth devices (android watch, pebble, fitbit, etc). Basically the headphones would drop whenever the phone communicated with another device, no matter how briefly.
-I also have Jaybird Freedom and Freedom Sprint bt headphones (the models they made before X's) and they do not drop even with tile, pebble, fitbit.
The X's seem to be very sensitive to other devices talking with the phone via BT. As a side data point, my factory stereo in a 2012 Kia seems the exact same. It will drop connection with my iphone (and my previous android phones) when it talks to another bt device. But with the kia radio (streaming music to stereo) you can hear some mini drops where the sound cuts out but the connection does not end . . . but after a few of these, it drops.
BT, IMHO, is a very mediocre technology and many issues pop up between various combinations of gear. But it seems like BT is becoming more common every day and we are just to live with it.
My Bluebird X's are totally unused now, which *****. I think they are otherwise a great wireless headset (especially with comply tips). I am very hesitant to buy some other BT headset as it might end up the same.