Swap motor with another axis. If it follows the motor it may be the encoder as you suspect. But make sure pulleys are not slipping, etc. (mark them to the shafts).
There is a coupling between the encoder and the motor. Is that tight?
Maybe a bad encoder?
No, I have not been to the office to look for encoder adjustment procedures.
The older machines had a different encoder. I believe the BEI was the better of the two. Had a few cases years ago where the older one was replaced by the BEI but nothing since.