Blackbaud Merchant Services (BBMS) does not automatically reject a credit card because the card has expired.  The request is sent directly to the issuing bank of the credit card.  If the credit card is still in good standing, the transaction will be approved.  If the credit card is no longer in use, then the transaction will be rejected.

Credit cards that have expired will process normally through BBMS.

If you would like expired credit cards to be automatically declined:
Contact Support and reference this article.