Mac Mini shutting down while asleep.

Question

I have frequent problems with my Mac Mini shutting down while asleep. Resetting the SMC doesn't seem to help. SMC firmware is the latest version. Hardware details are:
Model Name:          Mac mini
  Model Identifier:          Macmini6,2
  Processor Name:          Intel Core i7
  Processor Speed:          2.3 GHz
  Number of Processors:          1
  Total Number of Cores:          4
  L2 Cache (per Core):          256 KB
  L3 Cache:          6 MB
  Memory:          8 GB
  Boot ROM Version:          MM61.0106.B03
  SMC Version (system):          2.8f1
OS X 10.9.1

Answer 1

If you have more than one user account, you must be logged in as an administrator to carry out these instructions.
This procedure is a diagnostic test. It makes no changes to your data.
Please triple-click anywhere in the line below on this page to select it:
syslog -k Sender kernel -k Message CSeq 'n Cause: -' | tail | awk '/:/{$4=""; print}' | pbcopy
Copy the selected text to the Clipboard by pressing the key combination command-C.
Launch the built-in Terminal application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Terminal in the icon grid.
Paste into the Terminal window by pressing the key combination command-V. I've tested these instructions only with the Safari web browser. If you use another browser, you may have to press the return key after pasting.
Wait for a new line ending in a dollar sign (“$”) to appear below what you entered.
The output of the command will be automatically copied to the Clipboard. If the command produced no output, the Clipboard will be empty. Paste into a reply to this message.