Is your AC compressor in good working order? When the AC is switched off, the belt idles on the compressor pulley. When the switch is turned on, the compressor clutch engages the compressor pulley to the compressor internals. If the compressor is seizing, when you switch the AC on, the belt will be pulled around a pulley that cannot rotate. This will not last long, as it will burn the belt off. I would begin by checking the compressor.