Lumia 925 headphone became one sided with WP8.1

Try NOT using the Xbox player for a day and see if that helps. I had the same problem with the DP on 8.0 and 8.1 when using the Music player. Using Nokia Mix I don't have the issue. If I get the issue in Music, it will carry over to other Apps.

Try a clean boot an use only Nokia Mix to play back. See if it works for you.

That definitely doesn't work. I don't use Xbox Music on my 925 and only use MixRadio. I've had the problem on the phone plenty of times while listening to MixRadio.