In the Account Management system, make sure you're on the account you want to update and then press the Subscription button near the bottom of the page and start through the steps to subscribe an account.
When you get to the screen showing your credit card info, click on the link in the upper right corner that says, "Manage Accounts."
You should see a logo for your current credit card with a very small link next to it that says, "Edit." Click that link.
You should be able to change the expiration date for your card on the next screen that pops up. If you're only dealing with one account, you might want to just completely delete the card info at the bottom, instead of updating the info and pressing Save and Continue. I've read a lot of people say that they seem to have trouble getting the updated info to "stick." So perhaps just delete the card info completely, go back to the Subscription button for the account you want to renew and put the card info in from scratch, including the new expiration date.
Good luck.