Yep. That's what bothers me, as well: That for 45 minutes to an hour I have no idea that my monitor is not picking up my sensors. I'd estimate that could be enough time for a tow'd wheel to lock up and heat things to the point of combustion.
Apparently it was enough time for the OP's tire to blow and him not know about it. Who knows if he would have gotten a warning had there been repeater. (No, I don't fault him for not having one.)
According to Mike at TST, having a working repeater makes it more likely that the monitor will not lose touch with the sensors due to distance/interference/whatever. But there is still that possibility, I suppose, that the repeater could fail/come unplugged/become unwired.
I'd sure like to know the system's not doing what it's supposed to be doing alot sooner.
Still and all, I feel safer traveling WITH a TPMS than without one. Just not as safe as I used to. ;)