Well, there's no simple answer to that question, RTH. There are several reasons why they don't get challanged.
One, very rarely are they enforced against the sort of people who have the resources to fight it. To fight a law like that costs money, and a lot of it . . . or a very determined pro bono lawyer. Moreover, often the dog is killed halfway through the challenge, meaning the court will dismiss it as moot.
Two, in terms of constitutional issues, the key with BSL is something called rational basis review. A town is perfectly free to pass a law banning all dogs. If you don't like it, you can move. (I know that's absurd, but there you go) But to ban some dogs they have to show that all dog owners have "equal protection" under the laws. Unless the equal protection issue involves a distinction that is subject to special scrutiny, such as race, or gender or religious faith, the law is evaluated under what is called a "rational basis" review. Basically, is there a "rational basis" for denying owners of disfavored dog breeds "equal protection" of the laws . . i.e. to discrimate against them by confiscating and destroying thier property?
No, you say, there is no rational basis. I agree. Unfortunately, "rational basis" review is utterly toothless. As long as they can provide a reason, any reason at all, that is not clearly the rantings of a madman, its going to pass the review in most courts. A pile of news articles blaming "pit bulls" for dog bites is enough to pass "rational basis" review in most cases.
Now, some BSL laws have been struck down as "void for vagueness". Laws have to be clear enough that people can know if they are breaking them. So a law banning, say, American Staffordshire Terriers, is not void for vagueness. But a law banning "pit bulls" and giving a description so broad it could apply to dozens of breeds and hordes of mixes can be "void for vagueness" because there's no reliable way to determine if a dog is a "pit bull" so someone might not know they were breaking the law. Moreover, there have been enough DNA tests of purported pit bulls that turned out to be no such thing that some judges have taken notice.
So . .there's the short answer.