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This can be caused by having outdated third-party Mail plugins installed, or by using a copy of Mail that wasn't updated properly, or by not having the Mail application in the Applications folder.
Mac OS X v10.5.6 or later: Mail unexpectedly quits
I know it says 10.5.6 but the same rules apply.
Hope this helps,
This may also be due to the Sudden Termination feature built into OS X, which will effectively quit a process if the system is demanding resources. Mail can be a RAM hog at times, and if your system only has a few GB of RAM, then when other programs demand more and you have not been using Mail then the system will invoke Sudden Termination to quit it so more RAM is available elsewhere.
Do you have only ~2-4GB of RAM in your system? Check for this in the About This Mac option in the Apple menu, and if so then consider upgrading to more if your system supports it. Alternatively you can try quitting other applications to free up more RAM.
To see which programs are using the most RAM, open the Activity Monitor utility and choose My Processes from the drop-down menu. Then ensure Real Memory is checked in the View > Columns menu, and click this menu's title to sort the items by it.
Keep in mind that sudden termination does not fully quit the program, so Mail may still show up in Activity Monitor when you open it even though it may be closed from the Dock.