Hi Doug,
Plastic is prone to degradation by sun-light, eventually forming a matt (or even chalky) surface that holds onto dirt and won't take a shine.
The way to renovate the surface is to use a polish - like T-Cut - and not a wax. There is a difference between polish and wax - polish means a cutting agent that physically removes micro amounts of the surface, whereas a wax means a surface coating that promotes shine - companies that use the words "wax polish" in a product description are probably as dumb as their products.
Try T-Cut first, each time you use this it will remove the top layer of the plastic - which shouldn't be a problem on a plastic surface.
If you've used T-Cut and not got anywhere, try a more aggressive polish - one that removes more material with each application - look in the car body repair section of a DIY shop for these products.
Once the damaged surface has been removed, protect it with a good quality wax - the pastes have more waxes than the liquid products - and last longer.
Robert