It appears that one of the items on your car that is most susceptible to the elements and sun or UV damage is the convertible top. Without proper care they will fade, stain, yellow and crack similar to cloudy headlights. If this condition is not checked and allowed to worsen eventually expensive replacement will be the only option. There is an alternative which is restoration of the convertible top. Just like with headlight restoration, an item that was previously replaced at great expense can now easily be restored to like new condition.
Before proceeding with this article, be sure to check your owners manual for required car as some convertible tops are more sensitive or may require special products or coatings for maximum durability. If you do not already have an owners manual one can easily be purchased through your local new car dealer (for older models they may have to order it as it probably will not be in stock). It is also a good idea to have the owners manual anyway so you know the correct maintenance intervals, safety issues and everything you need to know related to your car.
Most convertible tops incorporate a plastic window or windows. These windows rarely are treated to withstand the sun and UV damage. For most, routine cleaning with specialized car wash soap and following up with some wax will usually do the trick. Be careful not to get the wax on the vinyl or cloth top material as it may stain or discolor it. For oxidized and cloudy plastic windows what we have found that works best is headlight lens restoration. When this treatment is applied to the windows, it removes the oxidation and film and restores optical clarity just like it does with headlight lenses. The results on plastic windows are amazing. Glass windows can be cleaned with regular glass cleaner and for stuck on debris a razor blade works wonders (do not use glass cleaner on plastic windows or parts).
Using a vacuum cleaner and lint free towels remove all dirt and debris around the top (this includes inside the back window where bugs and debris accumulate a long hose attachment works great here. Also do not forget to lift the convertible top cover and clean out the inside). Then look at the top and see what material it is made out of.