If this is an IMAP account and the missing mailbox was an IMAP mailbox, not “On My Mac”, the maibox and messages are stored on the server and are not available to be backed up in Time Machine, which explains why Time Machine may have mixed results at best trying to restore a single IMAP mailbox.

If this is an IMAP account there is an off chance the mailbox was not deleted but has disappeared on Mail mail because somehow it has lost synch, on the Mail menu bar select Mailbox ➭ Synchronize All Accounts and that should restore the missing mailbox. On the other hand if the Mailbox was deleted on your Mac it would normally be deleted on the server as well. In that case your best bet is to contact the account provider’s tech support and see if they can restore the mailbox from their backups.

If the account is a POP account or the missing mailbox was “On My Mac” then you should be able to restore it from Time Machine without difficulty.


"All you've got to do is own up to your ignorance
honestly, and you'll find people who are eager to
fill your head with information"
--Walt Disney