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This happened to me. I actually learned the hard way that Amex will immediately withdraw funds from your bank as if you are making a debit card payment. In other words, they withdraw their money for payments the same day, per their website "Payments must be received by 8:00p.m. MST to be credited on the same day." I made a payment later in the night, almost 10 pm Eastern and didn't think anything of it. The next day I realized the payment was attempted by AMEX the night before and I had not bothered to make my bank deposit..... so it was returned. I did explain to them that I was just a newbie and all and will never do it again. They kindly refunded my returned payment fee ($27) days later but they never forgot. I received the same message you got after I applied for another card months later.
no, I haven't applied again. I'll wait until next year. Good luck to you.