[Lowcountry idn]

So to confirme - they replaced all the sensors twice - the original and the second time - and its still the same problem.

I sincerely doubt its the BCM. It could be either the received - which is integrated with the remote door locks - do your FOB's work? Or it could be the BCM which holds the codes and communicates to the ECM, but I would expect the BCM to be causing additional issues as well, not just tire sensors.

Remote module antenna, BCM, ECM - are all solid state stuff. That kind of stuff sort of works or it doesn't - and there all multi purpose, so if its only your TPMS then I would guess also its the sensors. Just because the battery can send signals right next to the tire doesn't necessarily mean the signal is strong enough to be captured by the antenna.