The instance I had with a slipping servo was flying a new plane which was using parts from a crashed airplane. The arm had split opposite the side with the pushrod holes. When the surface moved under load, it would open up.. then grip the serrations at a different point on the servo output shaft. This made for an amusing shifting neutral.
Fortunately it wasn't my plane, so my concern was minimal, but I was able to get the thing on the ground and determine the reason for the bizarre behavior.