We put our booster on a 12v plug also. Previously we had it plugged into the jump box in the tow'd (not my idea) but we're going to put it mid-coach from now on, as suggested by Chuck at Minder Research. There just happens to be a 12v outlet there anyway.
Just for the record, I LIKE our TST system. It seems like some people around here think I'm denigrating TST or making derogatory comments about their product. That is incorrect.
What I don't like about TPMS systems (and apparently this is not a brand-specific issue) is that when there's a dropped signal from a sensor, it can take up to an hour for that information to show up on a monitor.
Yes, the repeated/booster SHOULD help with or resolve this. I'm just concerned about people who don't know they need one. They could have readings on their monitors that are an hour old. Look at what happened to the OP.
As said before, the systems aren't perfect and a TPMS doesn't make us bullet-proof, but I still feel safer traveling with one than without one.
We just have to be aware of the limitations of our systems.