Permanent magnet in ac motor
In a properly designed motor, no, they will not degrade. This sort of thing was a problem with older permanent magnet materials (if you are old enough you might remember the need for 'keeper iron' on the magnets at school) but with modern rare-earth magnets this is not a problem.

A permanent magnet is essentially a magnetic material with an extremely large B-H curve hysteresis. When you apply a large magneto-motive force (MMF) across the material, the magnet retains most of this force when it is removed. To demagnetize the magnet, or reverse the polarity, you have to supply a sufficiently large MMF in the opposing direction to 'snap over' to the other side of the hysteresis curve. In old magnetic materials, even the reluctance generated by the airgap between the poles could be sufficient to do this (hence the need for keeper iron), but with new materials the required MMF is so large that specialist magnetizing equipment is typically required.

If the motor is poorly designed, then it is possible that under transient conditions this could occur, but in most motor typologies the backing iron will saturate long before a sufficient field can be generated to demagnetize the permanent magnets. However, at a critical temperature permanent magnetization can be lost in most permanent magnet materials, so this remains a real risk if internal temperatures are not carefully managed.