Do stepper motors fail if not allowed to rotate?
Stepper motors (depending on how they are driven) are generally always on. You change the polarity of the signal driving the coils in a sequence to control movement. So leaving the motor powered is not going to damage it.

Now if there is too high of a load torque on the shaft - such as if you try and stop it spinning - the rotor will not be able to spin with the changing magnetic field. In this situation, the motor will start "skipping" steps, whereby you instruct it to move, but it doesn't. As you keep stepping, the field will move around and sometimes be aligned with the rotor and sometimes not.

This will probably not damage the motor, but it is not a good idea for a couple of reasons (maybe more)


While in this stall condition, the field will be constantly changing as you are stepping around which will cause a lot of vibration and noise. The vibration could be damaging to whatever the motor is mounted to and may lead to premature failure of your mechanics
Whatever control system you have driving the motor will usually have some form of internal counter used to determine the position. If it is a closed loop system (i.e. you also have encoders to verify that a step has occurred), this won't be too much of an issue (and in fact you could detect the stall and stop the motor). If you are using an open loop system which has no feedback (they assume that every step they send will result in movement), this stall condition will cause the controller to lose count, which may affect future operations.