I've always thought he just kind of slurred over the "a", like you'd do in casual speech, it came out like "f'r'a man". In the recording there's a tiny slight bit of a vowel after the "r" sound. I don't think he blew the line, just didn't speak it clearly.
Not a lot of people know that after his famous lines as he descended the ladder, Armstrong quietly muttered "and good luck Mr. Lansky". The few people who have heard the audio asked him about over the years, and he was never willing to explain ... until one day. "Well, you see" said Armstrong at a NASA publicity event, "when I was a kid growing up one of my neighbors were Mr & Mrs Lansky. I was playing on the street one day, maybe 8 or 9 years old, it was a hot summer's day and everyone had their windows open. Mr & Mrs Lansky were having some sort of argument inside their house - I couldn't hear much of what they were saying. But then Mrs Lansky must have moved closer to the window, because I heard her very clearly say "Oral sex? You'll get oral sex from me the day that kid next door walks on the moon!"".