One may come across instances where incoming mail from a mailbox (or mailboxes) might no longer be necessary to be imported into FoxBugz. This article explains the process of disabling mailboxes and therefore, stopping FogBugz from fetching mail and creating cases for those messages.
Go to the Avatar Menu > Mailboxes:
This will list the FogBugz Connected Mailboxes:
Identify the Mailbox that you want to disable and click on the "bin" icon under the "Delete" column.
You will receive a confirmation pop-up:
Once you confirm the deletion of the Mailbox, it will disappear from the FogBugz Connected Mailboxes list.