Sounds like you had one fail. Pretty common since they are battery powered, if you google "BMW TPMS battery" you will see all the folks who have discussed trying to change the battery. You have to replace the entire sensor. They are rated for up to 7 years but many have gone in the 4 to 5 year range. As someone stated, if you get a low pressure warning, it tells you which tire. But when the TPMS is not functioning you just get an error that does not specify a tire. Just saw that error when I had a spare on last week. Next time you get a low pressure warning look closely at the diagram of the car on the Idrive screen, my Wife pointed out to me that the wheel that is low shows up in a different color (orange or red?). I never noticed that in previous instances.
The tire shop should be able to use a handheld Tire Pressure Sensor interrogator, you walk it around to each tire and it reads out the wireless transmitter data. They are kinda pricey to buy yourself, and to be honest why would anyone bother to buy that device. The shop has to unmount/remount/balance the tire to get to it so it isn't a DIY repair.
The only other issue is that the TPMS control unit could crap out, I don't think that is common at all though. Only saw one instance in what I have read.
Last edited by tampamark; 12-24-2012 at 08:29 PM.