The most common reason for the motor to periodocly shut off like this is that it is over heating and the thermol protection system kicks in to protect the motor.
The most common cause for a motor to over heat; is the belt is simply to tight. You could have worn pillow bushings, but if they are causing that much pull on the motor you would hear a god awful noise from them.
To test your belt tension grasp the belt between your thumb and forefinger and apply light up & down pressure (approximatly 3 lbs). The belt should only move about 3/4 to 1 inch.
To adjust the belt varies, usually you will find a bolt that holds the motor mounting bracket. It is usually in a cresent shaped slot. Loosen this bolt "a little" and move the motor toward the pulley slightly. If you move it too much, just redo it until you can only move the belt as above. If the belt is too loose, the worse that can happen is the belt might slip a little.
To learn more service and repair information on evaporative coolers, visit:
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Larry Galpin The Cooler Doctor
Service, Repair & Enhance the Performance of Your Cooler Yourself and Save $100s Every Year!