All along, I thought this was simply because Musharraf was regarded as tough on terror. While I disagreed with this assessment, indeed, I felt that the Pakistani military would incubate the problem to keep the aid flowing, and only address it when it gets out of hand (see the Red Mosque incident), this at least made sense to me. However, it turns out the actual reason may be even more frustrating. An article from the New Republic makes the case.
Yet, facing a potential implosion in a nuclear-armed nation rife with jihadists, the White House remained unperturbed. In the midst of the general's crackdown, Bush called Musharraf a "loyal ally" and, improbably, "truly ... somebody who believes in democracy." Behind the scenes, the administration maneuvered to keep Musharraf in power, urging former prime minister Benazir Bhutto, recently returned to Pakistan from years of exile, to sign a power- sharing agreement that would have left Musharraf in charge of the country's security forces. Long after the United States would have abandoned most foreign leaders who abused their populations at great risk to American security, Bush not only stuck with Musharraf, but increased his support for him.
To some White House insiders, however, Bush's stubborn fealty toward Pakistan was no surprise. Over the past seven years, many foreign policy analysts have explained the Bush administration's controversial decisions as a function of ideology (namely neoconservatism) or the predilections of specific policymakers (such as Paul Wolfowitz or Donald Rumsfeld). But, in truth, one of the chief drivers of Bush's foreign policy has been the president's own tendency to personalize diplomacy. All good presidents develop relationships with their counterparts, but the former frat boy in Bush likes to quickly size up a foreign leader and then set policy based on his unreliable first impression. Unfortunately, this "great man" diplomacy has caused one policy disaster after the next. Bush's White House often puts so much trust in an ally that it ignores a leader's weakness or even perfidy, as with Iraq's Nouri Al Maliki or Russia's Vladimir Putin. Nowhere has this proclivity been more problematic than in Pakistan.
This is frustrating. According to this theory, the United States has remained close to Pakistan not for any geo-strategic reasons, but because Bush likes Musharraf that darn much.
Do I need to lay out how this is a bad way to conduct foreign-policy.
In Cruel and Unusual: Bush/Cheney's New World Order, Mark Crispin Miller argues (among other things) that Bush identifies with these rulers. He sees them as Bush-like people, talking about Putin as a fitness person etc. Our president sympathizes with foreign strong-men.