The left stick ball thing(TM) on mine popped "up and down" like it wasn't secured properly. Happened after a while and I just kind of lived with it. But I eventually just stopped really using it and didn't bother calling since it was well past the 90 days.
After talking to some of the MS people at E3 they said to just contact support and they'd take care of it, and sure enough they did.
I had this same problem and fixed it using a cotton ball and about ~10 mins of effort surprisingly. I had just lived with it because it never got in the way but then one day a YouTube video popped up in my feed about how to fix it, and it was surprisingly easy.
If anybody else has this problem and wants to fix it on their own:
You need a torque X security screw driver (~$6 at my local hardware store) and some cotton balls (pack of 50 for like $2, or if you paint your nails or live with someone who does, you should have some). It'll void your warranty but was really easy to repair and mine's been going strong for about a year since fixing it.
Basically you disassemble the plastic around the controller (theres like 8 screws if I remember correctly), popping off the face plate, and then take you stuff some cotton material around the metal piece for the stick, and then push the plastic piece back onto the stick with some cotton ball pieces. It basically just makes the grip tighter on the plastic topper for the stick so that ti doesn't pop up and down and stays snug. Re-assmble it and it should be good. While I was at it I used some alcohol to clean the bumpers and triggers.
You shouldn't *have* to do this for an "Elite" expensive controller but if you do have this problem and don't want to ship it back it was a quick fix for me. THe only real cost was the Torque X screw driver, I had to buy one at my local hardware store and bought the universal one that has multiple fittings. I think it was a Torque X s6 or s7 size. A universal one will do the trick and the YouTube videos of fixing it will tell the right size.