MacBook Air shuts down unexpectedly

Question

MacBook Air (2012) keeps shutting down unexpectedly. And then shuts down during start up several times before it works again.
I was getting an "Error: shrinkdb"  message in console for a while.
I tried reinstalling Yosemite which did nothing. I also tried downgrading to Mavericks which also did nothing.
I've verified/repaired permissions and the disk several times successfully with no change.
I've also got the message "unlink of file /users/***/Library/Caches/com.apple.Safari/fsCachedData" in console.
Also when repairing permissions I've gotten this message: warning: SUID file "system/library/coreservices/remotemanagement/ardagent.app/contents/macos/ardag ent" has been modified and will not be repaired

Answer 1

These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.
Launch the Console 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 and start typing the name.
In the Console window, select
          DIAGNOSTIC AND USAGE INFORMATION ▹ System Diagnostic Reports
(not Diagnostic and Usage Messages) from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar.
There is a disclosure triangle to the left of the list item. If the triangle is pointing to the right, click it so that it points down. You'll see a list of reports. A panic report has a name that begins with "Kernel" and ends in ".panic". Select the most recent one. The contents of the report will appear on the right. Use copy and paste to post the entire contents—the text, not a screenshot.
If you don't see any reports listed, but you know there was a panic, you may have chosen Diagnostic and Usage Messages from the log list. Choose DIAGNOSTIC AND USAGE INFORMATION instead.
In the interest of privacy, I suggest that, before posting, you edit out the “Anonymous UUID,” a long string of letters, numbers, and dashes in the header of the report, if it’s present (it may not be.)
Please don’t post other kinds of diagnostic report.
I know the report is long, maybe several hundred lines. Please post all of it anyway.