Repeatedly asking for CVV code

I have an account on Apple+. I have a valid credit card on the account. However I keep getting a CVV verification screen every time I want to watch something. I enter my info, I change cards, doesn't matter - it's a loop. Please let us know. Text from the message below. Thanks.

Verify Credit Card

You will not be charged. Enter the security code for your Visa •••• XXXX credit card to ensure that the account holder has authorized viewing on the web.