My Mail has the Quit menu item disabled, and it doesn't allow me to quit it.
I know that similar question has been asked here before, but it doesn't have any positive answer.
It happens very sporadic so I cannot understand what causes it.
The only way to quit Mail is to force-quit it in Activity monitor. After that mail works normally.
What I remember from day before is that I did try to move a group of mail to another folder using the rules and that got stuck.
Looking in the Console I find this as most recent mail activity. There is a huge report attached to it, so I won't publish it here unless requested.
8/1/13 9:16:44.356 AM sandboxd: () Mail(6153) deny file-issue-extension
Also looking in the Console from day before here is what Mail reported.
MBA with OS 10.8.4 and Mail 6.5