If the air gap of an induction motor is increased, the following will happen:
In summary, the maximum available torque will decrease, power factor will worsen and the motor will run with increased slip.
So it is always good performance-wise to run with as small an air gap as possible, which will reverse all of these effects. But if the air gap is too small, rotor cooling is compromised, and if the rotor expands through overheating (e.g. by exceeding the recommended maximum number of start per hour) the rotor can “pole” by rubbing or jamming with the stator. Not a pretty sight!
You may note that larger motors have better full-load power factors and less full-load slip than their smaller counterparts. This is mainly because their air gap is smaller as a proportion of the other linear dimensions of the motor.