Your TPMS light will flash for one minute then go solid when there is a malfunction detected in the system. With my TPMS, the light will come on when the tires are 10% or more under inflated from the spec on the sticker by the driver's door.
The other reason why the light will come on is that one or more TPMS sensors can no longer detect a PSI in one or more of the tires. Do you have a DIC? If so, when the light starts flashing, go into the DIC to the tire psi. You can scroll through all four tires. Most likely, you will get to one tire and it will show "- - " on the DIC. Meaning the system is not getting any reading back from the TPMS for that sensor.
From what I have read, the life span of a TPMS sensor is 7-8 years before the battery starts to deteriorate causing the sensor to fail and lose signal. The batteries are internal to the sensor and you cannot just replace the battery. If you have to replace one TPMS sensor, it is recommended to replace all (4) of the sensors at the same time. I just had to replace mine last year due to the same issue you are describing. This issue happened a lot to me during the winter months as the sensor was affected more.
Next time you have the flashing light, scroll through your DIC (if you have one) and see which sensor is not reading.
Do you know how to do the manual relearn process for the TPMS sensors? Every time you rotate your tires, you have to do the relearn process so the system knows where each sensor is located in order to provide you an accurate reading in the DIC when you get a low pressure warning or scrolling looking at tire pressures. This same process can be used when installing new TPMS sensors as well.