Payment Declined - How to Force Retry Same Card (Re-Charge)
Others have mentioned ways to do this that no longer work. Such as editing the card and adding a space in the name field then saving. Or giving links to Apple support pages where they say to delete the payment method and use a new one.
The fast fix is to go to Apple Account (top box in settings) click "Payment & Shipping" then "Add Money" then "Other" and send yourself $1 to your Apple Account balance.
Even though I wasn't able to download apps or make other purchases, it let me do this with the declined card. And within 5 seconds I got two notifications that Apple charged my card two items they had been trying when it was declined.
Hopefully this works for others, and if not let me know.