If the password is changed in your source email account, Outpost will not be able to connect to it to receive or send new messages until the email is reauthorized in Outpost. When this happens Outpost will display a notification banner at the top of the Mailbox Settings screen available to Owner and Administrator accounts:
Clicking on the blue "Reconnect mailbox" button along the bottom of the screen will reconnect and re-sync the mailbox. You will be prompted to re-authorize your source email address to work with Outpost (Gmail's message is shown below)
Note: You must be an account admin or owner to reconnect a mailbox.
Upon clicking "Allow", your Outpost mailbox will be reconnected to your source email account.