I took the NSA polygraph a couple months ago.  I passed on my first try.  And actually, I just received the call yesterday that I am finally cleared.  I'm waiting on the date for my briefing and then I'll start.  It took 3 months to go through the clearance process.

Read this thread for my experience:  https://antipolygraph.org/cgi-bin/forums/YaBB.pl?num=1286242505

I don't know what the odds of your passing the 2nd polygraph are, but it is not at all unusual for NSA applicants to initially be accused of "having problems," to be badgered for admissions, and then to be brought back for one or more follow-up sessions. For more on the polygraph technique used by NSA (the "relevant/irrelevant test"), see Chapter 3 of The Lie Behind the Lie Detector (1 MB PDF).

See also my commentary on the NSA polygraph unit's recent public relations video, which you may have been shown:

I had my first attempt at the polygraph for NSA as a step toward becoming an NSA Contractor.

Everything went well for the first part related to acts against the government which lead me to feel confident over the suitability questions remaining.

First I am a recovering alocolic who has not had a drink in 13 years and will not take presciption medications given to me for back pain.  Yes I was confident.

Yet I failed.  I was asked a number of questions and even confessed that I was a leadfoot and did not obey speeding laws.  I confessed that as a six year old I stole a 49cent matchbox car.   

Another test and another failure.  At times I actually felt the room was warmer and could feel the beeds of sweat forming on my brow, but I remained convinced that I had not done anything (ever) that would prevent me from passing this test.

I am scheduled for a second test and now wonder what will happen.

I do not need this job as I am employed, but I want the job.

What are the odds I will pass the 2nd test?