The behavior you're observing from your TST system seems strange to me. I have the TST 507 system with flow-through sensors and trailer repeater, and mine seems to respond very well. I'll generally see a cycle-to-cycle variation of perhaps 1 psig and/or 1 degF on a given tire once we're on the road and everything has stabilized under steady-state conditions.
You're right, though - if the TST system doesn't pick up a signal, it will display the last reading for quite awhile (probably to prevent "lost signal" nuisance alarms, which I've had when I forgot to plug in the repeater). I notice this when we unhitch from the 5th wheel and drive away without switching the trailer tire display off - the trailer tires will still be displaying the last readings obtained when I'm 5 miles away from the 5th wheel.
Rusty