The likely issue is that you have a card on file for your amazon account, but had been making purchases via the amazon website. If you didn't specifically associate a particular card with the kindle, or configure one to a one click setting for the kindle then you could face this issue.
There are a few easy steps to fix this though.
From your amazon account page on the computer,
First, go to Manage Payment Options:
there you can be sure your card/bank info is correct (right address, valid expiration date, etc)
From there, go to Manage Your Content and Devices:
On this page, click on the SETTINGS tab at the top right,
then you can from there set a default card to be used for one click purchases on the kindle.
Under Kindle Payment Settings, click on the Edit Payment Method button, and you can set the card you want used for your kindle purchases.
After that, reboot the kindle by pressing/sliding and holding the power button for 20+ seconds, and it should operate normally from there.
If it still doesn't take effect we'll look at a few more settings, just let me know.