Outlook 2010 and 2010+ versions seem to remove meeting request emails from your inbox once you accept or decline the invite.
How do I prevent these from being removed and keep them in my inbox?
Usually the meeting invite also contains useful information or things that need to be followed up later.
In Outlook, this is found under the File tab. Click Options, then Mail, and scroll down to the Send messages section. Uncheck the box next to Delete meeting requests and notifications from Inbox after responding