Unfortunately, there is no appeal process. I suppose you could write a second request addressed directly to the FBI Director. Although such a request is unlikely to be entertained, your letter should be added to your permanent FBI file and will document in the strongest terms that you do not concur with your polygrapher's accusation of deception.

In any event, even had you been granted a "re-test," the result would have almost certainly been the same as the first time: the FBI polygraph unit cannot politically afford to be seen reversing more than a handful of applicant polygraph results. Nearly everyone offered a "re-test" fails it. FBI polygraph "re-tests" are a sham intended to create the appearance, but not the reality, of fairness in a process that is blatantly unfair.

Even if you don't get a re-test, you still got a nice little gift from the FBI.  Whenever you now go to get another job in law enforcement and have to take a polygraph, you get to explain how you were not honest on your polygraph test for the FBI.  Afterall, polygraph tests are accurate in the 95% range, (as we keep being told).