Why does Airbook sometimes restart itself after shutting down?

Question

My MacBook Air sometimes restarts itself after I shut it down. At first I thought I was carelessly choosing the wrong command, but now I'm clear -- it's the Airbook.  Also -- I had thought this was unrelated, but now I'm not so sure -- it's been forgetting to start up automatically some mornings.  And yesterday at 3:19 pm it informed me that it was getting ready to shut down, "as instructed" (the actual instruction in the Energy Saver is for midnight).

Answer 1

From: Eustace Mendis
Sounds like a Broken Drive...
Most of the times this will be solved with a HardDrive Replacement
although,
you could try this
Restart your Mac and hold down the Command key and the R key (Command-R).
Keep holding these keys until the Apple icon appears.
This indicates that your Mac is starting up.
After the Recovery System is finished starting up,
you should see a desktop with an OS X menu bar and a "Mac OS X Utilities" window.
After you do this, select Disk Utility and run it.
On the next screen,
Select the hard drive in the left hand column,
the First Aid tab on the top, and click on Reparid Disk. (bottom left)
When that is done, click on Repair Permissions.
When that is done, quit Disk Utility and restart.