Allow me to piggyback on MRRSM's most recent post regarding TPMS and Trailblazers.
I don't have precise diagnosis details, but I'll share an experience that may help others reading this thread.
My Trailblazer started losing signal to a single TP sensor. It was intermittent and the pressure reading went from correct to zero and back to the correct PSI over the course of a days driving.
I'm a simple minded fellow and ASSUMED the issue was a failing sensor in that wheel. It was only affecting that individual wheel, so what else could it be, right? Wrong.
After purchasing a package of 4 tire pressure sensors and the learning tool off of Amazon, I had the sensors fitted at a tire store where they attempted to program them. However, after fitting those new sensors, there were now 2 sensors that would not communicate or program correctly.
The folks at the tire store warned me beforehand that the issue I was describing could be a communication issue between the car and the wheel sensors, not necessarily a failed TP sensor. Turns out they were right.
I replaced the Liftgate Module and was able to program all four TP sensors immediately. The liftgate module is the receiver for the TPMS and apparently can lose reception over the years. I happened to have a spare parts car in my yard for parts robbing, so the cost to me for the liftgate module was zero. The Chinese sensors, formatting tool and sensor installation at the tire store cost me $110. Maybe I didn't need them, that is the point I'm sharing with you in relating my story.
Rick