I have a 2002 Chrysler 300M Special with a similar issue. I had taken it to an Autobell car wash which ripped out my tire stems (no liability accepted as per their sign). Ever since then, the TPS has had issues. It started with ‘Service Tire Pressure System’. Took it to the dealer but the computer did not return any code despite the beeping and warning message. Three of the five sensors were replaced without resolution. Eventually, another dealership replaced the EVIC (overhead module) but then I got a ‘Tire Sensor Missing/Bad’ message. Chrysler got involved but both dealerships have given up as they cannot determine the problem and both claim they have spent too much free time on resolving the issue that I originally paid them both to fix. As they see it, I am paying them to ‘look’ at the problem - there is no guarantee implied that they can actually ‘fix’ the problem. This was my first Chrysler and American car for that matter and it will also be my last.
One last thing, they suggest I retrain the sensors periodically or whenever a message comes up using the magnet donut that comes with the spare tire - it is a simple five minute procedure using the EVIC module menu and is easier with two people. Place the donut on the appropriate tire until the horn beeps and then go to the next tire. Some people have told me that these TPS systems are notoriously faulty.