THE PROBLEM: After upgrading from NIS 2008 to NIS 2009, LiveUpdate began popping up in the lower-right corner of the screen every few hours, saying "Update Available". Under previous versions of NIS, LU just ran silently and automatically, never asking for permission. Now, clicking "Yes" led to a LiveUpdate Express list of components, and clicking "Start" initiated the update downloads. When they finished, installation began, but always failed with an LU 1812 error (trying to install "LiveUpdate Notice") followed by an LU 1806 error. A few hours later, the pop-up reappeared and the same things happened every time.
By contrast, clicking "Live Update" in the NIS window always worked.
Symantec Support's "Chat" technician bypassed the problem by turning off "Automatic LiveUpdate" in "Computer | Settings", but that didn't seem to be a good solution, since those updates are needed and I don't want to have to remember to do them manually.
THE CAUSE: There was a two-year old copy of the LiveUpdate components in C:\Program Files\Symantec\LiveUpdate", and it seems that its content ran instead of the current LU packaged with NIS 2009. The old copy didn't understand the new NIS and/or couldn't find needed components to be updated.
THE SOLUTION: 1) rename that folder to something else (it probably could be deleted, but renaming is safer). 2) Install the current version of LiveUpdate and reboot. (Installing it without renaming the original folder did not solve the problem.) Thereafter, "Automatic LiveUpdate" can be turned ON, and it will work properly without any pop-up requests for permission to run LU. You can install LU from here (the address in that link is: http://service1.symantec.com/Support/sharedtech.nsf/docid/1999051911110813)
Now, it's entirely possible that just renaming or deleting the old LiveUpdate folder, without installing the current LiveUpdate, would also work; but I didn't try that.