Both my front and rear urethane bumpers are loosing the shine. any suggestions on how I can bring them back so they shine like the rest of the car?

I replaced my front with a Flex-Fit. And flex fit does not always fit that good. On your urethane bumper, find a trustworthy paint shop that does urethane, fiber-glas work. Stripping takes a special stripper so you do not shrink or damage it. I would suggest stripping and painting is "on the car". Every Corvette made, back in the 70's that had the urethane bumper, one bumper would not necessarily fit another car. And maybe sometime they do. If you take it off, and if the stripping process is not done right, it can shrink, warp, and many other things that will make you wish it was left on the car. This was my experience, and not necessarily anyone else's.
Boatman

I have to agree with Boatman. Your original bumper covers will continue to deteriorate until there is nothing left and they fall off. Fiberglass covers will not fade differently then the rest of the car. You could try a claybar which would remove any oxidation and surface imperfections that could be present.