Had some time before the same problem. Mastercard has very high security standards in comparison to other cards like VISA. But when you use the Secure Code, it should work. But you must also look out, when you try to book much times with the same card and all the transactions were not succesful, Emirates black lists your credit card number and you will never more be able to book anything on emirates.com with this credit-card! (I had the same problem) So maybe this might be the reason, why you can't book.
Kind regards
Peter