I was denied for length of accounts (or lack thereof) when I applied for the Zync in January. Haven't bothered applying since, figured I'd wait until some inquiries drop off for me in December. I'm not sure what they (Amex) want for length of accounts, since I've been hearing 6 months or 12 months from various forums.
I did talk to a credit analyst at Citi roughly a week ago, she said that you have to have a minimum of 12 months for them. She said that cards that you've had for less than 12 months don't count as 'established credit' in their eyes until they hit that 12 month mark. I'd heard 6 months for Citi before, but the credit analyst was unwavering in her insistance that the credit lines won't count as 'established credit' until they're a year old.
Granted, that's Citi and not Amex, but she was trying to pass it off as being an industry standard rule. She was all business and sounded pretty serious about the rule. Chase told me a year minimum in the past too, so that seems to be the safe bet.