Davidson wrote on Jan 22^nd, 2008 at 3:39pm:

I am in a similar position - made it to Phase II and was told that I failed one section of the polygraph. I sent a letter in requesting a second polygraph, and was told I "did not meet the criteria required and will not be afforded further consideration..." Is there an appeals process? Can you offer some suggestions as to the content of the appropriate letter? Thanks.

Without going into details, I can tell you that they do read every appeals letter that you send to them.  The problem is they won't reveal exactly what their criteria is for determining when to give a retest.  It's difficult to argue your case when you don't know what they consider to be important.