AI CS6 (64bit) stopped working error

Method 1:

Also you may refer to the below provided article and the support link and check if the steps provided assist you resolve the issue -
http://kb2.adobe.com/cps/408/kb408849.html

Method 2:

You may check if you face the same issue accessing adobe application in a clean boot state. To perform the clean boot follow the step 1 mentioned in the below article and then try checking in this clean boot state -

        http://support.microsoft.com/kb/929135
 

If the issue gets resolved check which non-Microsoft service is causing the problem; referring to the article and following other steps.

After you have finished troubleshooting, follow these steps to reset the computer to start as usual:

a.     Click Start, type msconfig.exe in the Start Search box, and then press ENTER.
If you are prompted for an administrator password or for confirmation, type your password, or click Continue.

b.     On the General tab, click the Normal Startup option, and then click OK.

c.     When you are prompted to restart the computer, click Restart.

Method 3:

If the issue persists, I would suggest you to contact the adobe support for assistance on the issue.  You may refer to the links below for assistance-

http://www.adobe.com/support/

http://forums.adobe.com/index.jspa

Hope this helps.