I'm so sorry to read about your experience,
@magusmccormick. I can't imagine anything more frustrating than to do your best and "leave it all on the floor" on an interview, only to get a denial letter.
One small comfort: Most interviewers will tell you that while there are processes that are followed during the interview process, so much of it is determined on a gut level. I was reading somewhere that the decision to hire or not is determined within the first few minutes of an interview - and the rest of the time is spent validating the decision.
Know that you probably did nothing "wrong" (although it's certainly a good idea to take a good hard look at your presentation - we can all improve) - it could have been all about your interviewer. You have to remember that you were asked to interview a second time...and there could be more interviews on the horizon at Apple for you.
Email/call your recruiter and let him/her know that you're still interested in being considered for positions at Apple - and you'd be appreciative if s/he'd keep you in mind for other opportunities within the company. It never hurts to ask.
Good luck!