In the photo in post #4 there's a gap between the red buffer and the driven section of the coupling, either the ballscrew moved down or the driven section of the coupling moved down.
If the driven section of the coupling can move down then it's not tight enough and would also slip in rotation, and because more torque is required to lift Z than lower it the axis would slowly slip down.
If the coupling driven plate is slipping then stripping, cleaning, then reassembling with a stud & bearing fit compound may provide a temporary fix,

- Nick