The correct answer is A) rotor contact with the stator. Periodically checking the stator-to-rotor air gap clearance in an induction motor with a feeler gauge helps prevent the rotor from making contact with the stator. This is crucial because if the rotor were to come into contact with the stator, it could lead to severe damage to the motor, including potential failure of the motor. Maintaining the proper air gap clearance ensures that the rotor can spin freely without rubbing against the stator, which helps preserve the motor's efficiency and longevity. The other answer choices are incorrect because they do not directly address the purpose of checking the stator-to-rotor air gap clearance. Checking the air gap does not specifically prevent electrical damage to the bearings (B), damage to the motor bearings (C), or axial misalignment of the rotor (D), although these may be related maintenance considerations for the overall health of the induction motor.