The tire pressure monitor is very crude on our cars.
It simply works using the wheel speed sensors to sense when any one is rotating faster than the others then trips the warning. It will not reset until you manually reset it. It will also trip the warning display if the front underhood power supply at the fuse panel is disconnected.
My friend has a newer Jeep Grand Cherokee that actually has pressure transmitters built into the valve stems that sense pressure and then wirelessly transmit to the PCM. A much more expensive system.