The 2 oxygen sensors "behind" the precats in the exhaust are part of the catalyst monitoring system. They detect the oxygen coming through the cats and if isn't within spec, you will get a P0420 or P0430. If you have a bad sensor in front of the cats, this could cause your mixture to go crazy and this will decrease the life of your cats.
IMHO, if you are having sensor problems in front of the cats, then you may have damaged a cat and that is why you are getting a P0420.
As far as the sensor problem, I would check the wiring to the sensor itself, then I would check all the components that make up your air/fuel ratio. Check the intake to make sure all is well (filter, MAF, TB, Manifolds). Also check the fuel system (Fuel Filter, Dirty injectors) and the ignition sytem (Plugs, wires and coil). If something is wrong with any of these components, it can screw up a sensor and thus a cat.