Frank,

You can expect that the agency whose polygraph operators branded you as a liar will never hire you or grant you a security clearance. Your polygraph failure does not necessarily preclude you from ever obtaining a top secret clearance with another agency. However, it will make things more difficult. Your polygraph failure is a permanent record, and it will be shared with any other agency that may consider granting you a security clearance.

There is no meaningful appeal process for polygraph failures with any federal agency. What you can (and should) do, however, is to write a letter to the agency contesting the results. This letter should be added to your file and will document the fact that you contest the polygraph operators' accusation of deception.

Our government's reliance on the pseudoscience of polygraphy is both foolhardy and immoral. They use it as a cost-savings device. Some applicants make disqualifying admissions, obviating the need for a background investigation. But in the process, many truthful persons such as yourself are wrongly branded as liars and suffer irreparable career harm as a result. Meanwhile, spies, saboteurs, and terrorists can easily fool the polygraph using simple countermeasures that polygraph operators cannot detect.

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How does one even know if the reason for a rejection for employment at the federal agency is polygraph related or not?  Certainly neither the CIA nor the NSA provide any explanation for not hiring an applicant.