I apologize that you are experiencing this issue! Have you tried accessing Constant Contact from another browser? Are you experiencing any error messages when trying to save your account information? Is the email address a verified email address on the account? If the email address is not verified before the attempt to update the billing information the changes will not save. I went ahead and took a look at your account and this does appear to be the issue.
Follow these instructions here to verify your email address.
Then to update your billing email address please follow these steps: