I have problems with the headphone jack, I lose connection and sounds like he improperly connected, I had the moto x 2013 and had the same problem at 9 months of use, and moto x 2014 are having this same problem a month of use
I had problems with my Droid dna like this a couple of years ago. Turned out the problem was lint from my pocket in the head phone jack. I blew it out and also poked around with a paper clip and it was fine after that. Maybe check to see if that is the cause.
I'm having the exact same issue with my 2013 and 2014 Moto x. I've narrowed it down to any pair of headphones that have any inline controls. Look at the jack and I bet you have 3 lines. If you have a pair of headphones with 2 lines (standard headphones) that should fix the issue. I don't know how they can fix it, but I think this is what you're dealing with.