Why my tire pressure light stays on

The tire pressure light comes on, this indicates a low tire pressure or may have a bad sensor. Also, it may be caused by a monitor system malfunction. 
By having the proper tire pressure, you will get better gas mileage, also it will slow your tire wear.
If the tire position on the wheel was changed by doing tire rotation, the tire sensors may need to be reset. You may have to go to an auto repair shop for calibration by an experienced mechanic.
If your tire pressure warning light comes on when you are using a spare, this might be the cause because most of the time the spare tire has no sensor.
Cold air is denser, so filling the tires on cold mornings means that they are overfilled, on the other hand, if you filled your tires on a warm day a sudden cold day makes the tire pressure too low.