Prevent Outlook meeting requests from auto-deleting
Another option is create a rule for messages of Kind "Meeting Request" to be copied to an "Invitations" folder in your inbox.

Steps that work on my version of Outlook.


Create an Invitations folder. 
Highlight message that is a meeting invite
Click on the "Organize" toolbar
Click on the "Rules" icon
On the little menu that pops up, click "Create Rule..."
On the rules dialog, the first field will say "From". Change that to "Kind". 
The next box will say "Encrypted" (as in Kind is Encrypted). Change that to "Meeting Request"
Use the minus sign to delete the sent to and subject rules (the next two rows)
Change "Do the Following" from "Move to Folder" to "Copy to Folder"
Change the folder name to "Invitations" or whatever you called it in step one
Uncheck the box "Do not apply other rules..."
Click ok