????
White is pretty much the easiest color to maintain, and reflects away the most sunlight and UV...
Which is why I'm a bit puzzled. If you're having trouble with discoloration and fading, with a WHITE car, then I run the risk of upsetting you by informing you that you're doing a horrid job of general and basic upkeep, regardless of whether the car sits out or not.
You shouldn't have to wax the car much more than once every 3-4 months. That should be more than adequate. However, your problems MAY be due to your washing. Do you wash yourself? Or do you run it through a car wash? If you are using a harsh detergent on your car, or running it through a harsh wash, you're basically stripping the wax or poly right off the paint prematurely... Your discoloration may also be caused by the products you're using.
Bottom-line, white should be simple. It hides scratches, and reflects/shuns UV and fading. If you're having these types of troubles with white, you'd be pulling your hair out with red or black.
Share with us what you're currently using for wash and wax, how often, etc.. A cover is always a good idea for during the day, if you have to park in an unshaded parking lot for work... But at night, it's really not accomplishing anything beyond protecting the car from the odd cat, or if you're parked under a tree... Other than that, there's nothing going on at night that your finish needs protected from.
Hope you don't take my criticism too badly, but something's amiss here!
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If you've got an issue, here's a tissue...