The result of the CVC, address, and zip/postal code checks are ones that most payment processors pass directly through from the cardholder's bank.
If the zip check has failed, it's because the bank is telling the payment processor that the zip code does not match the one it has on file.
If the cardholder has recently moved, it may take their bank a while to have the correct zip code on file for them. If the cardholder hasn't moved recently, they may wish to call their bank and confirm that the information their bank has on file is correct. Using the zip/postal code that the bank has on file for this card will stop this particular error from happening.
For people that are using Stripe as their payment processor, if the payment is being declined and you'd like to accept it, you may want to see if the “Decline charges that fail zip code validation” setting is on.
You can verify this from the Account Settings page in Stripe. If you're confident accepting payment from this customer when the zip/postal code doesn't match, you may wish to turn that option off temporarily to allow you to accept their payment.
Have any questions? Please submit a ticket here.