If replied emails are not automatically updated to the corresponding case, most likely, you have not set Helpdesk Agent add-in to track and monitor your primary mailbox (Inbox and Sent Items) folders. You can do so from under Helpdesk toolbar > Settings > Personal Settings > Automatic Email Tracking tabs.
By default, Helpdesk Agent add-in only tracks and processes the emails associated with existing cases from your primary mailbox. So, if you use other accounts to reply to cases or if you receive emails from callers to other mailboxes in your Outlook, then you must specify those mailboxes too. Enabling this would force your Helpdesk Agent add-in to look for incoming/outgoing emails in those mailboxes too.
NOTE: If you and other technicians have opened the same mailboxes in Outlook, only one of you should enable Helpdesk Agent add-in to track those mailboxes. If multiple technicians have the same mailboxes tracked, it could lead to data duplication in the cases.