As an electrical engineer, my approach to troubleshooting this problem would be to start with two principles - Occam's Razor which states that the simplest explanation is most likely the correct explanation, and basic motor theory.
What others have said is correct - there could be a problem in the speed control. But before going there, you might want to check to see if there is a less drastic cause.
This lathe uses a DC motor, and with DC motors, the speed is a function of the product of the voltage applied to the rotor multiplied by the voltage applied to the state. However, this is likely a permanent magnet motor in which case the rotor flux is fixed by the permanent magnets inside the motor. So speed fluctuation can only result from variations in the stator voltage which comes from the speed control box. I think the perception is the the speed is surging from normal to some higher point, but is it possible that over time the 'normal' lathe speed has actually become lower; in that case, you may have simply compensated by turning the knob to force it to speed up, but what is now happening is that it is intermittently returning to that higher normal speed. That would imply that the normal voltage being received by the motor is reduced from what it should be, but is intermittently popping back up to its normal level. Strange - yes, but that could result from a loose connection between the controller and the motor.
My lathe (a Turncrafter) is similar to the Jet, and the connections to the speed control is by means of a plug. A few years ago, I added an external reversing switch which put an additional plug into that connection between the speed control box and the motor. Occasionally, if one of those plug connections works loose, the additional resistance in the circuit causes the voltage delivered to the motor to drop causing a drop in 'normal' speed.
So - before concluding that you need a new speed control box, check for loose connections. If that's the cause, the fix would be much less expensive!