WP Tasty uses the popular and secure Stripe to process debit and credit card payments.
The following is taken from Stripe's explanation of why some cards are declined.
Declines can happen for a variety of reasons. When we submit a charge to the customer’s bank, they have automated systems that determine whether or not to accept the charge. These systems take various signals into account, such as your customer’s spending habits, account balance, and card information like the expiration date and CVC.
Since these signals are constantly changing, a previously successful card might be declined in the future. Even if all of the card information is correct, and your customer previously had a successful payment, a future charge can still be declined by a bank’s overzealous fraud systems.
Unfortunately most declines are generic, so we don’t have much information as to why a charge was specifically declined.
If all of the card information seems correct, it is best to have your customer contact his or her bank, inquire for more information, and ask for future charges to be accepted.