My experience is almost identical to that another user whose thread has now been tagged "Solved" and closed:
Norton IS 2010/2011 crashing during system full scan
In this thread the user solves his problem by reinstalling Windows XP 
I hope I can avoid doing that. I'd be more inclined to uninstall NIS 2011 and use another AV product. A technician did respond to the user with instructions for a possibly less drastic solution if the problem reappeared.
reese_anschultz wrote:
If the problem does return, please look in the Norton/Symantec Errors section of your logs to see if any entries are present around the time of the crash and provide their information (contect-click on the entry and copy it to the clipboard and then from the clipboard into a message.) Also, if it occurs again you may wish to try disabling scanning of container files as a temporary workaround since the crash appears to have been related to that functionality.
In my case after first noticing that the NIS icon was disappearing from my task bar tray while refusing to restart, I decided to try running a full system scan. The scan aborted with a error message generated by the One Click Support program that suggested reinstalling NIS 2011 after employing the removal tool if the error message continued to be generated during a full system scan. After I reinstalled NIS 2011 the error message did not reappear, but the full system scan continued to abort before completion. Access to NIS 2011 continued to remain available with the presence of the NIS 2011 icon in the task bar tray.
I suppose my next step is to try the suggestion made by reese_anschultz and examine my error log entires.