By far, the most common reason for a card to be declined that I see is a billing address mismatch. Our system checks the billing address of the card (among other things), so if you have moved recently, or have both a street address and a PO Box, it may not match and be declined for that reason. You can have books shipped to an address other than the billing address on your card, but the billing address must match what your credit card company has on file.
Your particular credit card may have other security measures in place which could cause it to be declined, such as buying online from a vendor that you have not previously purchased from. There are all sorts of reasons why a card could be declined. My system only allows me to see billing address mismatch or “other – contact card issuer.”