I wouldn't know who issued the card, purchases are done through a gateway like mygate. I asked these companies as well but none can help. These guys are just going to keep on doing it. The worst thing of all is that Visa 3D is used and the payments are going through. 3 Months down the line I get a chargeback.
So I take it you are the merchant here and not the card owner whose card was stolen. That changes things ever so slightly.
That you'd have to take up with Visa then. They charge the merchant a fee in return for effectively guaranteeing the transaction. Do check your contract with them beforehand though.
I've tried all the banks, they simply say they can only blacklist the cards. It still doesn't catch the crooks. I was even thinking of starting a thread where everyone and anyone who has had any fraudulant attempts in there shops publish the names and e-mails of these people who try to buy with stolen cards, maybe it will help another store somewhere along the way, I don't know.