Mailboxes that were added to timetoreply using the bulk add method, should very rarely lose authentication with timetoreply, however, if one does, you can follow the same steps initially used to bulk link the mailbox, to re-authenticate it again.

Go to Tools > Mailboxes > Add mailboxes (multiple at once), select the mailbox from the list of mailboxes presented to you and then click on Save Mailboxes.