Is there a setting so that when an Outlook meeting invitation is accepted the invitation is not automatically removed from the Inbox? I often accept invitations and then realize that I needed some information about them. It would make it easier if they stayed in the Inbox and behaved more like everything else in the Inbox.
Yes, it's a configurable option in Outlook.
Outlook 2003 and 2007
Tools > Options > Advanced E-mail Options (2003)
Untick Delete meeting request from Inbox when responding.
Outlook 2010 and 2013
Go to the File tab and click Options. Select the Mail tab in the left pane.
Untick Delete Meeting Requests and Notifications from Inbox after Responding.
Now when you accept a meeting invitation it should keep the original mail in the inbox.
On Outlook online, go to Options -> All Options -> Settings -> Calendar, then uncheck "Delete meeting requests and responses that have been updated" then press save.