Is the Z axis coupling broken? Crack can hide nicely in those wire cut ones if that's what you have.
A coupling slipping on shaft is another thing, that no amount of tightening will fix. Pull it apart and examine closely.
A screw digging a hole in the shaft and moving back and forwards in the fretted groove it has made.
Couplings that clamp on the shaft are generally less of a problem.
A loose wire in a connector to the stepper is a likely electrical problem.
Super X3. 3600rpm. Sheridan 6"x24" Lathe + more. Three ways to fix things: The right way, the other way, and maybe your way, which is possibly a faster wrong way.