In case anyone else encounters this issue in the future, I thought I'd add a recent finding:
I've been having this issue frequently near a BMG extruder outlet. I'd cut the tube a couple of times to give it fresh material to clamp onto, which did help a bit, but the issue was slowly getting worse.
I had a couple of the E3D Bowden fittings spares laying around and thought I'd try replacing the inner fitting. I cut 1/4 of it off to get it out, but was actually fairly surprised when I got it out.
Bowden Fitting Covered with PTFE Residue
The original tube (also from Anycubic) had left some residue on the Bowden clip - you can see it in white. This was essentially coating the clip in PTFE as well, which substantially reduces the friction holding the tube in place (PTFE on PTFE has the nearly the lowest friction coefficient possible). I switched the tube to some leftover Capricorn tubing and changed out the fitting - I've noticed the difference immediately despite the smaller outer diameter of the Capricorn.
TLDR?
Public Service Announcement: Throw away your Anycubic PTFE tubing and replace the Bowden insert if you're having this problem.