After a few minutes of printing or movement one of my Z axis motor stops moving. Then I switched off the supply and after waiting a few minutes I again tried moving the motor. It works for a few minutes and stops again!!!. What could be the problem?

Probably something is overheating.

Check the temperature of the driver chip; you may need to add a heatsink and/or cooling fan.

Also check the temperature of the motor itself; it shouldn't be too hot to hold your finger on it. You may need to adjust the current going to the motor down a bit.