How can I tell if Jotform has cancelled a registration due to payment declines?

It won't appear in your submission data that the registration has been cancelled. You should see this in your payment processor account. Let say if you use PayPal, you should see cancelled registration in your PayPal dashboar.

Jotform only integrates payment processors so users can use them in Jotform's form.

Let us know if you have any questions or if you need further assistance.