Layer shifts can take an otherwise excellent print and in a very short time turn it into a useless piece of plastic. It can be incredibly frustrating when it happens, so here are some ways to fix it.
The nozzle hits parts of the model
If your print has strong overhangs and your printer lacks cooling, it may curl up and keep the nozzle from moving over the area without bumping into it. This can easily result in the axes not being able to do anything other than skip steps and therefore get out of sync with the calibration.
To prevent this from happening again, you can improve the part cooling fan setup on your printer to prevent the print from curling up. If this does not work, try activating the Z-hop feature which lifts the nozzle a set value each time the printer travels between points.
Check lack of power to motors
If you can keep the motor from moving its axis by holding the carrige lightly, you can be pretty sure that this is what causes the problem.
Proceed with caution; turn off your printer completely before proceeding, and follow the instructions at own risk.
On most printer motherboards (the electronics for the printer), the "current" (power) to the motors can be adjusted by turning small knob (potentiometer) with a small screwdriver (avoid touching other parts of the system board as it may damage it permanently). Turning clockwise turns up the power and strengthens the motor's ability to keep the axis running. Rotate in half turns until the axis runs effortlessly. However, keep an eye on the temperature of the motor during the next couple of print as it may get hot if it gets too much power and destroy the motor. Should it get hot, you should turn the potentiometer slightly counterclockwise to prevent it from getting too hot.
Check for loose connection to motor
Check if the plug in the motor is fully seated. If the vibration from the printer causes the pins to lose contact between the plug and the motor, it will stop it from spinning shortly and the miss steps.