A comment on his suggestions:

Lower profile wheels are not designed to not turn slower, the effective rolling diameter is the same, it is a larger wheel with a shorter tire sidewall height.

There may be other issues with those wheels and the physical size of the sensor, but if the wheel was originally offered it should work.

It seems to me that either a sensor has failed, or the controller that processes the signal from the sensor has failed. I would get a diagnosis to see which it is, and decide when you see the cost to repair whether it is worth it to you.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue