I'll be poster #83 to clarify. 
- Some rare people appear to be eligible for a CLI immediately.
- Many people are eligible for a CLI after 60 days (the after part is important, which is why you will see Amex days always referred to as 61, 91 and 181).
- Any customer-initiated credit line increase that is granted resets a 180 day moratorium clock for all American Express cards held by the account holder. (An automatic CLI does not reset the clock.)
- Any customer-initiated credit line increase that is declined with a reason other than something that translates to "you asked too soon" resets a 90 day moratorium clock for all American Express cards held by the account holder.
- Credit lines can be reallocated between revolving American Express accounts online as often as every 30 days, as long as you leave a minimum of $500 per card. However, many people report being unable to do so if the donor card (the one you are lowering the limit on) has been opened for less than one year.
Hope that helps. I received a CLI on my Blue in January and applied for the SPG card in March. I attempted a CLI at activation, at 61 days, and at 179 days - all denied because "American Express requires at least 180 days between credit line increases across all cards held by an account holder." Unless you are denied for a real reason, your counter will not be reset.
