The battery in the wheel sensors last about 10 years or so.
I had a 2010 XC60 that had TPMS codes. Code for a wheel sensor, replaced, drove, return to customer.
Customer called the next day, TPMS turned on, on the way home. Code for another wheel sensor, replaced.
I drove the car 10 miles up the interstate, TPMS turned on. The wheel sensors tested good with the beep beep tester. I started reading in VIDA about how the system works. In the TPMS PDF page 3, If the system, RKE, does not register all 4 wheel sensors in 10 minutes of first driving, it sets a code and message. Called customer and asked, did the TPMS turn on at 10 minutes of driving, yes it did. To verify, I erased TPMS codes, did not have too, just start a new drive cycle, it turned on in exactly 10 minutes. Replaced the RKE fixed it.
Drive for 10 minutes and see if the TPMS turns on. This may or may not show that your RKE is failing, it is a test. You could have more than 1 problem. You need the TPMS beep beep tester to check the tire sensors.
A friendly tire store might test each sensor. Autoparts store might have a TPMS tester, hoping to sell you a new wheel sensor. Make sure that your tire pressure is above 36 psi since it has turned colder. Sometimes we would have to set tire psi at 40-43 to make the light turn off. We also had to have the engine running, set tire pressure to 38 and the message turned off in 1 mile. It is a process to fix stuff like this.
The below alarm stuff, you need VIDA to go in and see what set the alarm off.
A better OBD reader should see this also. This info is helpful so that you are not throwing parts at it.
Info about the alarm system,
Diagnostic functions Alarm info
General
The central electronic module (CEM) is the main unit for the alarm function. In the control module are alarm function diagnostics. For information about diagnostic functions, see Design and Function, central electronic module (CEM).
Reading off the alarm cause
Different stored values can be read off using this function:
Alarm cause. Last stored input signal that triggered the alarm.
Not triggered. The alarm has not been triggered since the last reset.
Voltage drop siren.
Vehicle tilt sensor
Motion sensor
Driver’s door
Passenger door
Left rear door
Right rear door
Trunk lid / Tailgate
Hood
Open-circuit in the communication between the central electronic module (CEM) and the siren.
Unauthorised start attempt
Heartbeat sensor (for vehicles with heartbeat sensor).
Alarm status, fault in vehicle tilt sensor. The value can be True or False.
Alarm status, fault in siren. The value can be True or False.
Alarm status, fault in motion sensor. The value can be True or False.
Alarm status, fault in heartbeat sensor (for vehicles with heartbeat sensor). The value can be True or False.
Alarm status. The value can be the following:
Activated
Deactivated
Triggered
Alarm cause, table. Reading off the 8 last alarm causes and the time when they occurred.