The outside temp monitor is located on the passenger side of the vehicle, just in front of the radiator and behind the bumper it is mounted on a bracket to sample air prior to the radiator. It has a weather proof connector, if the sensor isn't functioning, either there is a broken wire in the wiring harness, the sensor has failed or the connection is only partially made. Since the connector is weather proof, it can appear to be connected when in fact it isn't. I would pull the connector out, inspect for water or damage, then plug it back together making sure it is fully seated.
The sensor does not work in a 'gradual' way, it either works or it doesn't. My car was in the dealer for some air conditioning work, they had to pull the sensor for some reason and neglected to fully seat the sensor connector upon reassembly. We noticed it not working when we arrived home from the dealer. I called the dealer for assistance in finding the sensor, while awaiting call-back, I went on the internet, found out where the sensor was located, went out to the car, found the connector not fully seated, re-connected the sensor, turned the car on and it was functioning normally. No driving, no waiting, it either works or it doesn't.