Newer cases and future cases (especially white ones) have/will have a better manufactured composition of plastic.Most of the time this applies to plastics not metals but unless in a dirty/dusty environment and long period of exposure to the sun (which the radiation makes the discoloring) it will take at least 10-15 years until discoloring may appear. Even when there is smoking in the room or house it can discolor.So unless the case is frequently exposed to sunlight like next to a window or someone is smoking in your house it shouldn't discolor at all.
It also depends on the cases good quality plastics and metal. Check carefully in reviews or before buying the case.