In reading the article you cite, some reasons for this happening, despite its dubious morality, are:
—While most requests for child brides come from Mexico, the majority that are approved come from Middle Eastern nationals. That means there's a combination of cultural and religious acceptance, at least among those who practice it, and the United States has had a hard time when it comes to sorting out Islamic differences between freedom of religion and the law. Even, admittedly where there shouldn't be a moral equivalency.
—In order for this to work, underage marriage needs to not only be acceptable in the country where the child bride is from, but it also needs to be legal in the state where she will reside. Many states have the legal marriage set at 18, but also allow for certain exceptions. It's these exceptions which are allowing, or aiding in permitting this to continue, even though the specific result is probably unintended.
—In many of these cases, parents and family are complicit. Even in the United States, minors are not afforded the same privileges and freedoms as an adult, and so as long as a parent is giving permission, the governing body (state or federal governments) will look the other way. If there's evidence of child endangerment, or something else, than the government may step in, but again, religious freedom and what is constituted by it can be a thorny issue.
—There are those in the U.S. Congress who want to shut down this practice by closing what they call a loophole in the laws. We can only hope that they can find a way to do so that won't open the door for something else, be it religious censorship, or something else bad.
—Wondering when this might actually be fixed is a good question. We are living in a strange time where a lot of what has been considered socially if not morally unacceptable is now perfectly permissible. As those social or moral moorings erode, it opens the door for many other practices to be considered, if not allowed. Without clear boundaries, an anything goes kind of attitude forms, and it becomes even harder to stop things that only years ago would have never happened, let alone be considered.