Each of my tires is properly inflated (approx. 31 psi cold) but the TPMS indicator won't turn off. I assume I have a bad sending unit in one of the wheels. The car is CPO, so I'm not terribly concerned, but is this common?
What do you mean "it won't turn off"? If a sensor is bad then it won't send any particular pressure at all or it will send an obviously bad one. Did you just add air to a low tire? They may take some time to reset, like 5 minutes or more of driving.