I read the post by "undesirable candidate" and feel I am in exactly the same boat.  I recently underwent a poly for the FBI for an analyst position.  Here are some of the things that happened to me and some questions I have for you all.
Before I had even gotten comfortable in the chair, the examiner told me I get one chance and if I failed, I would no longer be considered for the position.  The situation was stressful for me already and having him say that made it even more stressful (if that was possible).

I then proceeded to answer all of his questions truthfully (I had no reason to lie to anything).  After three series of questions, he tells me I "failed" and would I like to continue by having him write out any statements.  I told him fine and proceeded to clarify the drug use (6 times total in my life with marijauna).  He then proceed to call me a drug dealer (which I denied), a drug user in the past 3 years (which I denied since the last time I had use was almost 7 years ago), and  that I might have been recruited by some foreign intelligence to infiltrate the FBI and get their secrets (which, of course, I denied).  I left there thinking that I would probably get a second chance with another tester but I got my form letter this last week telling me that the job was rescinded.
I have asked for an appeal but have not heard from the person who was my "Applicant Coordinator".  Last week, I got a call from someone else in the FBI wanting me to come in for an interview for another job.  I explained the situation to him and was told that he would find out about the appeal process for me and whether or not he can even interview me since I had "failed" the poly.

What I find funny about all of this is that I have a clearance pending with the CIA (the contractor I was going to work for ended up losing the contract before I was to start but I had finished the process).  During that process, I had "failed" my first poly and was asked to come back the next day, which I then passed.

Also, I know that the background check had started on me because at the PSI, the agent told me that there were already initials on parts of my application showing that they had checked those items off.  Also, my boss got a visit by an agent and the agent also interviewed four of my co-workers.

Why doesn't the FBI allow a second poly for those people who get so worked up and stressed that it must throw off any of the needles on their machine?  Also, it was stated that they do the polygraph first and then do the background check after a pass.  From my experience, that isn’t true.

Also, by failing this one poly, does that mean I can never be considered for an FBI position again?  I know for a fact that I have 6 applications that have gone past the initial phase and are now in the respective departments being reviewed.  I would hate to think that my only chance, ever, at getting a decent job doing some interesting and mind stimulating work (not to mention important to our country) would be stopped because of this one “fail” even though I have that clearance pending with the CIA.

Any and all information would be helpful.  Do I have any recourse at all or should I just throw up my hands and move on?  I am pretty upset about this.  Thank you all ahead of time for any assistance.