2007 TB - Service Tire Pressure Monitor

I have a 2007 Trailblazer with the upgraded tire pressure monitoring system giving tire pressures for each tire through the driver info center. Some time ago I started to get sporadic loss of signal from various TPMS sensors. I replaced all the sensors assuming they were losing battery power. This worked for about 2 months when the LF sensor lost signal permanently. I replaced the "bad" LF sensor during a tire rotation putting the new sensor in LR position. Within hours the LF sensor lost signal again. So it appears to be the TPMS signal receiver is the culprit - not the sensors in the tires. Can someone tell me where the receiver is located? Is it part of a larger control module? And am I on the right track?