While I haven't had the warning light stay on, other than to say that the TPMS system was recalibrating itself, it has sometimes taken a few minutes (4 - 5 minutes) before my adding air to the tires has registered. For example, my TPMS (the at-rest function labeled TPC on the computer) might say "-1" for one of my tires. I add some air, checking to see how much I have added, and then turn on the ignition again to check. Sometimes it still reads "-1". I turn off the ignition, remove the key, and wait a few minutes. It usually gives an accurate reading after the second check.
Jim