Depending on what version of Outlook you are using;
For Outlook 2003/2007: Click Tools, –> Options, –>E-mail Options –> Advanced E-mail Options. Clear the Delete meeting request from Inbox when responding check box.
For Outlook 2010: In the File tab, click Options. Select the Mail tab in the left pane. Untick Delete Meeting Requests and Notifications from Inbox after Responding.