Is the account IMAP? What mail provider?

IMAP. Local ISP and WAVE cable.

IMAP may be using IDLE command, which means it is overriding the Account settings you mention. The IDLE command is a extension to the IMAP protocol that lets the IMAP server notify Thunderbird when there is new mail by sending a command over the existing TCP-IP connection. If your IMAP server supports that you don't have to manually check for new mail or have Thunderbird poll for new mail every x minutes.

Try this: 'Tools' > 'Account Settings' > 'Server Settings' for imap mail account or right click on imap mail account name in Folder Pane and select 'Settings' then select: 'Server Settings' for the imap mail account

click on 'Advanced' button Uncheck the "Use IDLE command if the server supports it" option. click on OK click on OK to close Account Settings.

Thanks. I have unchecked IDLE and it seems to have stopped the downloading every X minutes, but it is still downloading every time I sign on.

just a reality check here. You subscribe using a mail protocol that is designed to synchronize mail and folders with the mail server. Then want to stop it doing what it is designed to do.

Have you considered using POP which is just a download of the inbox and nothing else?