In the middle of a job, the z-axis lost some steps and continued engraving 0.5mm deeper. Which kind of settings do I need to adjust in order to avoid that. Will it be best to reduce the speed or the acceleration of the stepper motor?

You need to tune the steppers such that they won't skip for the work you intend on doing with your machine. Find the velocity of the motors where they will skip, then set the max velocity 20%  - 30% below where they skipped. Then find the acceleration value where they will skip and set the acccelration 20%-30% below where they start to skip.

Accuracy and reliability are more important than speed. Use of high feed rate will cause the stepper to skip if it doesn't have the needed torque to do the work.

RICH