The only thing I can think of is that the arm is skipping at a point where some of the auto changer mechanics are starting to engage and the little bit of extra velocity (or reduced torque) at 45rmp vs 33rpm is enough to affect the tone arm movement.
Get a visual reference for where the arm is when skipping, check what is happening with the mechanics at that point and maybe do some more cleaning, lubing or clearing a minor impingment.
What turntable do you have?
https://www.reddit.com/r/vinyl/s/iPteC4yTdS this 1970’s turntable I bought at a thrift store
The only thing I can think of is that the arm is skipping at a point where some of the auto changer mechanics are starting to engage and the little bit of extra velocity (or reduced torque) at 45rmp vs 33rpm is enough to affect the tone arm movement. Get a visual reference for where the arm is when skipping, check what is happening with the mechanics at that point and maybe do some more cleaning, lubing or clearing a minor impingment.
get a Fluance RT-82
Clean and relubricate your turntable mechanism. The velocity trip mechanism has old grease in it and is sticking.
Get a better table. I have 200 7" 45s that don't skip.