If the battery finally dies in one of the senders, the light comes on and stays on.
I THINK the light comes on if the pressure in any tire goes below 25 or 26 pounds. I also believe it comes on above 38 or so pounds, but I'm not sure. (Mine came on at the Dragon a year ago, one tire was down to 24 and others were around 29).
The standard pressure is 34 or 35 psi, if your tires went down to about 30, I don't think the light would come on. I don't know if a dealer can read what sensor has failed or not.
The base models had no TPMS, and I wonder if that is why one car was destroyed at the Dragon last fall. I have always wondered if he didn't have a soft tire - with his car being a base model, he'd have no warning, and the accident played out like there may have been a soft tire that made a bad combination with tall, wet grass.
GET IT FIXED.