From the U.S. Air Force Academy website:

The status of your security clearance can be affected, but it is not automatic. The outcome depends on the circumstances that led up to the bankruptcy and a number of other factors, such as your job performance and relationship with your chain of command. The security section will weigh whether the bankruptcy was caused primarily by an unexpected event, such as medical bills following a serious accident, or by financial irresponsibility. The security section may also consider the recommendations and comments of your chain of command and co-workers. This is an issue that can be argued both ways, so as a practical matter, your security clearance probably should not be a significant factor in making your decision about whether to file bankruptcy. The amount of your unpaid debts, by itself, may jeopardize your clearance, even if you don’t file bankruptcy. In that sense, not filing for bankruptcy may make you more of a security risk due to the size of your outstanding debts. By the same token, using a government-approved means of dealing with your debts may actually be viewed as an indication of financial responsibility. Eliminating your debts through bankruptcy may make you less of a security risk. There is no hard and fast answer here, with one exception: it never hurts to have a good reputation with your co-workers and your chain of command.

Basically, if you superiors want to get rid of you, they will use either the bankruptcy or your debt as a reason to pull your clearance. If your superiors want to keep you, they will use the bankruptcy as a reason to keep you, especially if the debt was caused by a one time event.

Also check out this article about security clearances from an attorney who specializes in it.