I've had several occasions of the receiver losing contact with a sensor, and it does indeed take about an hour for the notification. One thing I learned the hard way is that a GPS receiver can emit interference that leads to sensor signal loss. I solved this with an external antenna for the TST receiver positioned well away from the GPS. Other times when I've lost contact it has just been a mystery. When I suspect loss of contact, I shut the TST receiver off for a few seconds which does blank all the pressure displays until a new report is received.
My first thought to address the problem is for TST to add to each pressure/temperature display a timer that whould how old the reading is.