I have this exact problem as well with my iPhone 5 and Jaybird Bluebuds X. I've used dozens of Bluetooth devices over the years and have never experienced anything like this before, and this only seems to happen with this specific pair of headphones. I've test this on multiple headphones in this model (I lost them twice) and tested on my wife's iPhone 5 as well. You'd think I'd buy a different pair at this point, but the sound quality is above all others I've tried and I love the minimalist style of just ear buds on a string.
I find this infuriating and I've done many tests to see what I can find out. Here is what I've found:
When I connect the Bluebuds to my iPhone, I sometimes see the Ringer Volume display pop up. It's not every time, but it's often enough to notice.
When connecting, the ringer volume is set to the current ringer volume or the volume level the headphones were at the last time they were connected, whichever is lower.
If I raise the volume on the headphones, disconnect, then reconnect and the ringer volume is unaffected.
Let's say I had the headphones at 50% volume and the ringer at 75% volume; if I disconnect the headphones and reconnect, the ringer volume will pop up showing that the ringer is now at 50% volume. If I increase the headphone volume to 100% and reconnect again, the ringer volume stays at 50%.
Let's say when I leave for work in the morning I play some music on my headphones and have the ringer volume set to 100%, then as I get into my office I drop the headphone volume down to 25% before I charge my headphones. After work, I connect my headphones again and listen to music on the way home and go to sleep later that night. Guess what, the next morning I'm late for work... Why, you ask? Because my iPhone alarm is going off at only 25% volume. This is now my nightmare.