While your concern is understandable, in most cases, the card issuer's decision is final for all parties and cannot be appealed. Submitting evidence is the appeal phase of a dispute, and there is no subsequent appeal phase.
The issuer's decision is final in both directions. This means if you lose a dispute, you cannot appeal the loss. However, if you win a dispute, the cardholder cannot appeal their loss and must also abide by the issuer's decision.
Some card networks (specifically Visa and Mastercard) do have a lifecycle that goes beyond this initial loss, called "arbitration," but we do not recommend our clients appeal to it for two main reasons:
It's expensive, generally costing over $100 to initiate, with an additional fee of $500 that the loser pays.
Business win rates seem extremely low, even relative to normal dispute win rates.
Finally, it's important to note that the card networks are the authorities for how their card networks are used, but the card network dispute process is not a court of law.
Depending on the circumstances of a dispute, if you and your customer are within the same jurisdiction, it may be possible to seek relief in a small claims court or other civil forum designed for this purpose.