Franki41 wrote on Jul 24^th, 2016 at 8:44am:

Hello everyone, I’m just trying to find some information. What could about this (We have been notified by the Office of Internal Affairs that you did not complete a favorable polygraph examination; therefore, your tentative offer of employment is being withdrawn.) Can I reply and if so, when? Could I appeal this...

There is no meaningful appeal process for those who fail the CBP polygraph. However, you can and should write a reply to the person who sent the rejection letter contesting the polygrapher's accusation of deception (assuming that is, that you were truthful and were falsely accused). This letter should be added to your file and will document the fact that you disputed the outcome of the polygraph.

With respect to reapplying with CBP, I don't know the answer to that. If you can find out, could you post the answer here? I don't know whether CBP will in practice hire anyone who in the past has failed a CBP pre-employment polygraph "test."