First one would have to define the charge-back policy within their contracts. Then a determination of fault would have to be identified by either parties in that contract.
The problem with using credit cards for payments is the ability to have the payer request a charge back based on evidence "X". Since you missed a deadline, does it state in your contract agreement or other form of project acceptance that there would be a charge back if the deadline was missed? In this day and age I do believe that every business should have ways to protect themselves, especially if you are dealing with international clients.
Was there any correspondence from you as to the potential to miss a deadline? There are too many unknown variables to determine the proper placement of a policy such as this. Most standard agreements will have a "mediation before litigation" clause in them to avoid the predicament you are currently in. Best of luck.