It sounds like you didn't really fail the polygraph the first time, but were simply brought back for a second round. This is common practice in agencies such as the CIA and NSA.

In any event, during your next polygraph "test," you'll no doubt be asked about any prior polygraph examinations you've had. At that time, you can mention your prior polygraph experience.

It would be a mistake, however, to offer excuses for why you might not pass or might be sensitive to a certain question. Such excuse-making will be interpreted as a sign of deception.

For more on polygraph procedure and what to expect, see The Lie Behind the Lie Detector.