By default, Outlook deletes meeting request mails once you've accepted or declined the invite. This is designed to help you reduce clutter in your Inbox, and you can recover them individually if you like from your Deleted Items folder (as long as it hasn't been emptied).
If you prefer to hang on to these invite messages by default - say, to maintain a more complete e-mail history with your correspondents - you can toggle this option off.
In Outlook 2010, this is found under the File tab. Click Options, then Mail, and scroll down to the Send messages section. Now uncheck the box next to Delete meeting requests and notifications from Inbox after responding:
In Outlook 2007, you'll find the similar option Delete meeting request from Inbox when responding under Tools, Options, Preferences, E-mail Options, Advanced E-mail Options.