This whole thing sounds extremely similar to my poly at the CIA a few years ago.  When my tester pulled out the "you're having trouble with this question" bit, I reacted differently than you.  Instead of being on the verge of tears, I approached the verge of punching the guy out.  (I didn't, obviously.)  I had to come back for a second poly, which was a much calmer event administered by a woman.

If I could do it all over again, I would know going into it that it's all just a mind game.  As long as you don't let them beat you at the mind game, you win.  They don't really care about the question you're "having trouble with".  They want to see how you react under pressure, when you're confronted.  If you explode, or break down.. you're weak and can't be trusted.

My $.02