So I wanted to make a thread about this same issue since I couldn't find anything similar. Finally stumbled upon this one somewhat on accident. I think this issue becomes more interesting since we are now just out of the warranty period for launch consoles. I'm just going to copy and paste the thread that could not come to be. Keep in mind that this was typed up before I found/read through this thread:
Is anybody else having an issue with either of the analog sticks not always recognizing input? I was playing TLoU Saturday and noticed that when moving forward with Joel he sometimes slows down or stops moving outright for a brief moment, then goes back to full speed. This persists for my entire time playing. Sometimes he will completely stop in place for a second plus before moving again. It's even worse if I make any slight side movements, and I can forget about attempting to zig zag through an environment. The issue began happening with even more frequency when I played for a few hours yesterday.
I know there is a one year warranty on all PS4 hardware, but unfortunately I am a few days outside of the warranty period. For some reason I thought I was well beyond the warranty period (didn't realize the PS4 came out on the 15th, today is the 17th). I called Sony support and tried everything I could to reason with the rep, but it seemed pretty clear that there was nothing they could do as they would need proof of purchase to verify the hardware was in warranty.
What bothers me the most about all of this is that I feel like I've barely played my PS4. I played a couple hours a night most days of the week for about a month when the system came out, then a couple days a month for a few months, and I eventually had months go by without turning it on. I haven't put much use on the controller relative to how long I've owned it, but [almost] within a year it is becoming borderline unusable. I did a few minutes of Google searching and found that I was not the only person with this particular issue, but fortunately the other people who had this problem were within the one year warranty period.
The main reason I'm making this post is to ask for advice on what to do. I'm wondering if there's any way to repair this issue myself. I doubt it's as simple as buying a new analog stick and throwing it in there. I would rather not have to resort to dropping 50+ on a new controller but feel that I have no other choice right now (perfect timing after shelling out for DA:I and GTAV).
Any help is much appreciated.