You don't have enough information posted to make a really good evaluation, i.e. 3 phase or single phase, how they are powered and controlled, gearing / belting etc., but here is my attemp with what you told us:
Are these on VFDs by any chance? Sometimes people use VFDs on spindle drives because they want 3 phase motors so they can do simple reversing, braking and speed control and they only have 1 phase power available. Unfortunately, if they didn't know what they are doing and used cheap VFDs without Vector Control, they can easily stall at low speeds. That happens quite a lot.
If you are not using VFDs, you may have a bearing problem in the shaft of the drill head and as it heats up, it starts to seize. Changing the motor would not solve the problem and it may not show up as a damaged motor, especially if your overload relay is working properly. By the way, are the overloads not tripping off? Something else you didn't say. They should trip off long before the motor burns up!
If they are single phase motors, is the motor shop checking the start caps and the speed switch to make sure the starting capacitors are not still in the circuit?
There are plenty of other possibilities if you tell us more. We don't charge you by the word you know.
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