This functionality was working but stopped. I can move by right clicking the mail item and selecting Move and then selecting my archive folder.
After a bit of research all you need to do is press the Esc key a couple of times and the drag and drop functionality returns!
This occurred after upgrading an Outlook installation from Outlook 2007 to 2010 using an existing Outlook data file.
I resolved this by closing Outlook and launching Outlook.exe from the command line with the “cleanreminders” argument:
C:’Program Files’Microsoft Office’Office14’OUTLOOK.EXE /cleanreminders
Note: Office14 in this case links to Office 2010. The Office iteration is different by version.