How Doesn't the No Fly List Violate Due Process?

I happened to read a blog post by Kevin Drum just now about the no-fly list, the thing where the U.S. government gets to decide that so-and-so isn't allowed to fly on planes, at least not for flights that involve U.S. airports or something. This specific story is about a person who was put on the no-fly list completely by mistake. The government discovered that mistake. But it did not fix that mistake, for nine years. It kept the person on the no-fly list, and thereby effectively banned from the country (because the last flight they let her take was from San Francisco to Malaysia), for nine years, knowing that she was not a terrorist for almost all of that time. Yeah. U! S! A!

And I wonder, not for the first time, how the hell the no-fly list doesn't violate the Due Process Clause. There is, as I understand it, no way to challenge being placed on the no-fly list. You can't even bring a habeas motion, 'cause you're not imprisoned. Now, apparently the woman involved in this story did sue the government, and got herself removed from the no-fly list by court order. But due process is not a question of mistake. People are deprived of their right to air travel by the effectively arbitrary decision of some minor executive official, with no notice and no opportunity to be heard. That sounds like the epitome of a due process violation. The only possible argument to the contrary, it seems to me, would be that getting to fly on airplanes is not a "liberty" within the scope of the Due Process Clause. But I really doubt that argument would actually fly in court, especially since we've got this whole thing called "substantive due process" that reads the word "liberty" to include things like the right to use contraception. Is there a reason why no one's brought a suit alleging that the entire practice of the no-fly list is just flatly unconstitutional, mistake aside? And if not, well, someone should do that.