There are a number of things that could be the cause of the problem, but it would be helpful to know more information. First, which pulley speed range are you using? For the greatest mechanical output power as well as torque, you should use the low speed range for everything except for small stuff like pens and bottle stoppers. Second, what is the approximate spindle speed when the problem occurs? The power is lowest at slower motor speeds. That particular lathe model with 1.5 HP motor is pretty wimpy on power anyway, but if you happened to have the drive belt on the high speed range and had the speed control dialed way down, that would be the worst case scenario for bogging the motor down.
Based on your indication that the performance has been degrading over a long period of time, i would suspect that the motor is dying. My opinion is that particular motor is marginal for inverter duty, especially if you push it to the limit at slower speeds and even worse if the drive belt is in the high speed range. Running the motor slow and under heavy load for extended periods is bad because the motor will get very hot due to inadequate cooling. The other factor is that because of the way that inverters operate, the voltage to the motor will have high voltage transient spikes riding on top of the supply voltage. The more heavily that the motor is loaded down, the greater the amplitude of these transient spikes. These spikes can easily exceed 1000 volts and eventually cause internal arcing in the motor windings. The classic symptom for this kind of internal arcing failure is a gradual decrease in motor performance typically over a period of many months. The effect can be so subtle that it might go on for a while before a problem is suspected.
If the motor has a thermal overload switch, it is also possible that the thermal switch is defective. Whether it can be replaced is unknown to me. Often low cost motors aren't designed to be repaired. These days, "low cost" is sort of a euphemism fur a motor that retails for under about $500.
If you want sticker shock, look at the cost of industrial motors.
Diagnosing a problem over the Internet is mostly guessing and speculating and wild haired ideas so it would be best to contact Jet to see what they have to say. Arbitrarily replacing parts can be an expensive way to solve the problem.
