If you look under Tools > Account Settings. Open the Server Settings page for the account you want to stop downloading. Uncheck all the options to download at startup or at different intervals.

I had already tried this. Problem still continues. I have unchecked both "at startup" and interval options.

If the email account is no longer valid, you could just copy the message folders to Local Folders and delete the account .

You want to uncheck all 3 boxes for downloading, including the one for immediate notification. When I did that on an old account, it did not try to contact the server. However, the suggestion to move emails to local folders is a good permanent solution.