Since I did not watch the series from the beginning, I am not certain about the answer to this question. I was under the impression that if a fighter lost a fight, he was out of the contest, yet Peter lost his first fight and is still in the hunt.
Was he allowed back for another try like Ahmed, or what??

He was allowed another try, just like Ahmed was, because Jeff had the chicken pox.

I didn't agree with method of replacing a boxer that had to leave the show by bringing back a loser that lost his fight, would have been better to bring in next runner up (I'm sure there were some) than to let a loser back for another try. Defeats purpose of show.