Reducing give in bi-polar stepper motor axel
What you describe is called 'backlash'.

The data sheet for the motor shows that it is a gearbox output, with a fractional degree step angle. As such, it is unlikely you are moving the motor itself, all of the movement will be due to the tolerances of the gear teeth.

Preloading the output shaft with a spring (for non-continuous rotation) or a torque motor should remove most of the effect of backlash.

An alternative is to move away from stepper motors, use a servo with an absolute encoder on the output shaft, which will drive the motor such that the output shaft is always maintained in the wanted position.