Many of us suffer with this problem and up until recently I have been reapplying bumper restorer after each time I wash the car. I became frustrated at this process and eventually looked for a new answer to the solution. I came across one talking to my local mechanic.
You need to clean the whole car and then when it is dry get a DIY heat gun and gently heat the bumper up. (the sort of one that you use to remove gloss paint work). DO NOT LEAVE IN ONE PLACE OTHERWISE IT WILL MELT THE BUMPER!, ensure the heat gun is gentle moved across the bumper at all times. Suddenly the white marks and discoloured areas of the bumper will turn black!
PLEASE NOTE THAT ALL ADVICE GIVEN IN THIS POST IS USED AT THE OWNERS RISK. NO RESPONSIBILITY WILL BE TAKEN IF IT DAMAGES THE VEHICLE.