If you do not want to automatically delete a meeting requests or notification or after responding then you can disable this feature using Outlook Email Options. Click on the File menu –> Options link navigate to Mail tab on the left hand side and scroll down Send messages section.
Un tick the check box with label Delete meeting requests and notification from Inbox after responding. Click Ok to save the changes. Now if you accept any appointment requests or notifications, the requests will not be automatically removed from the Inbox.
Demo Video – Disable automatic deletion of meeting requests in Outlook 2010