"based on your history with credit card balance transfers, American Express welcome offers, introductory APR offers, or the number of Cards you have opened and closed, you are not eligible to receive the welcome offer, intro APRs, and intro plan fees."
My spouse just received this message when applying for her 4th Amex. The others are actively used and have been open for many years.She has no history of opening/closing for bonuses or balance transfers. FICO is 840,so no issue there either.