Glitches from wirewound potentiometer
Adding a heavy duty RC filter (1 M * 100nF) will help reduce noise while pot is moving, but a bad spot is always going to be a bad spot.

I ran into the same problem with variacs under daily use. At some point the element had no conduction at the bad spot, but micro-arcing of current from using the same spots over and over again was the culprit, so every two years I had to replace them.

I did not have this problem with the pots you use. A 10K resistor in series with the wiper would reduce any shoot-through currents when the pot is at extremes of range, and maybe the op-amp conducts or clamps voltage close to their supply rails.

I did switch to 1K pots to reduce sensitivity to noise, but I never had one with bad spots even after ten years of heavy use, but I used conductive plastic potentiometers, not wire-wound.