Then I got the idea that what was really wrong was that the clear coat was gone. I tried a little cear touch up paint to test the ides, and it worked! I went to the local auto parts store and bought a can of Duplicolor clear for $8. I masked off the metal work, so that only the rubber bumper was exposed and laid down 3 coats of clear before the can gave out.
Here is the result:
After a couple of days, I rubbed it in with some polishing compound to bring out the shine and there you have it. No need for an expensive paint job and no more embarrassing faded nose - and for only $8!