Nexus 5 user here. I've had similar issues. It used to happen many, many times a day on the last firmware but after the latest, my disconnects are few and far between. It started acting up just the other day, disconnecting a lot again for no apparent reason. No new faces or apps anything. This is the only issue that makes me question why bought the Pebble if I have to keep putting up with this.
try enabling accessibility toggle in android for pebble and try again
this fixed the bug for me on kitkat, it may fix the problem if exist on any version.