If a user reports their purchases as fraud, the first thing I do is BAN the user account associated with the report.

I don't want that user to ever come back on my site and purchase another thing.

Can they come back with a different account and use the same credit card all over again?

Thank you 🙂

Yes, they can from what I know. Unless you specifically block them on Stripe. I think that's doing by refunding as fraudulent. Perhaps an IPS Staff can clarify.

Would be better suited for a support ticket for an official answer. But as David said: I wouldn’t expect this functionality to exist. If you ban an account you ban an account. You can ban their IPs along with it, but there is no (visible) feature to do the same for payment data. 

Banning an account does not inherently ban their credit card number from usage.

@SJ77 you might be able to notify your payment gateway to set up fraud rules.