I'm a little confused. Did the OP book and actually fly on any of these tickets? If they were all eventually cancelled prior to flight time, I don't see where AA is really out any money, other than some nebulous opportunity loss for not being able to sell the seat while it was in this payment limbo. Moreover, AA bears a lot of responsibility for not properly validating the CC at the time of purchase and rejecting the sale then.
That said, I do agree that AA is completely justified in cutting the OP off from the system. One or two tickets booked this way could legitimately be considered to be a mistake. Repeated bogus bookings are clearly deliberate and abusive. And, frankly, pretty weird behavior. Any vendor would cut him off under the circumstances.