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Double-check that all of the information is correct, including the postcode.
Try using a different card if the problems persist.
Apple does use a really strict security feature, and some banks will flag a transaction due to an amount or fluctuation of multiple sales going through the same card in a single day, so the problem may be with your bank rather than with Apple.
As I said, Apple does use a really strict security feature which other sites do not use, so that is the likely reason why.