Engine Cooling problem
2003 Chevy Cavalier 4 cyl Front Wheel Drive Automatic 140000 miles

i recently started overheating in stop and go traffic. I noticed that thought the engine was very hot and the AC was on but the fan was not turning. I checked the voltage at the fan plug while the engine was running (AC on) and i got just over 13 Volts so i assumed the fan motor was bad and i replaced it. Immediately after i installed the new fan everything seemed to be back to normal, (engine hot or AC on, fan running). After several days i am getting higher than normal engine temp again. Again i checked fan with ac on and it is no longer turning. When i replaced the fan i was very careful not to over torque the bolt holding the fan to the fan motor shaft. I am wondering if there is another problem with the system that is causing my fan motor to go out. Is the 13V to high? i spun the fan with my hand and it seems to turn freely.

Thanks for your help.