I ran into a bit of a puzzle the other day. When I was inflating my tires in a balmy 9 degrees F the left rear tire stem gave up the ghost and my tire went flat in short order. I then replaced it with my spare after much swearing and cursing due to the cold temperature. When I started my car back up I got a left rear tire low pressure warning message even though that tire was now my spare. Note to car: no kidding, the tire was completely flat. It took another drive cycle for the car to recognize the flat tire was now my useless spare.

I am getting too old for the frigid temperatures and having to put up with changing tires in 9 degree F weather.

 

It does takes a bit of time for the system to realise that the wheels have moved position, I believe. As I understand it the system doesn't monitor all the sensors continuously and simultaneously; it interrogates them individually in sequence, so it takes a bit of time for the system to catch up.

Somewhere it does say that it's only an under-inflation, slow puncture detection system.

 

Mine took a long time to clear a similar situation.
The spare tire back in the trunk, after replacing the flat tires air sensor.
Car recognized flat tire was fixed, light went out.
Flat tire was put in the trunk (boot).
Car saw the spare was flat right away.
Flat repaired, & back in place
The warning light kept coming for quite some time.
Warning me to take care of the flat tire in the boot every time it was started.

 

I had a similar issue. Spare TPMS LOW. After installing new valve in my spare, no luck. found out it was the module. Ordered one (new not used), installed, and dealer could not program. Found out it had already been programed (used) and was faulty. Dealer took it back and asked if I wanted to save some $. They put my old one back in and programed the car to think that it didn't have a spare tire tpms. The original module flagged all other wheels good, just could not communicate with the spare. This fix doesn't bother me as it saved me some big cash, dealer didn't charge to program, and I'm in the boot enough not to need the TPMS. Free repair. Someone naughty purchased new module, and returned their old one.