My tire pressure sensor has always reset itself when I inflate the tires to the correct pressure. This time the light has remained on. I have checked the pressure of the tires when they are cold.

Could be bad sensor,one way to know is to remove battery postitive cable for a few minute,s and see if it go,s out,if not bad sensor.

You can usually reset the sensors if for some reason they need to be reset. one way is to go to tire shop. They have a little handheld machine that will reset them as they go around the car. another way on MOST cars is to deflate each tire in a specific order around the car after putting key into ignition and pressing certain buttons until horn beeps. USually this method is outlined in the manual for vehicle if it can be done. I know on come GM cars you turn key to "on" and press lock and unlock on the key fob at the same time and hold until horn beeps, then you start with driver front tire and deflate until horn beeps, go the passenger front and deflate until beep and so on. sorry I dont have specifics but like I said, if this method is possible it should outline it in the owners manual under "TPMS" section.