The only thing I see in the system log which is not normal is an occasional SONAR definitions error - but no errors logged for failed LU attempts.
Symhelp shows nothing scary - just a couple of warnings about not being on the latest version, and pending reboot, and the fact that we don't have some of the AV subcomponents installed (e.g. Outlook plugin), etc.
There's certainly nothing being reported in the main symhelp diagnosis which differs from any healthy systems we have.
It seems to me that there's a corruption of sorts in the LiveUpdate engine, and it can't run, but it's not being captured in logs (bar the failure to create log entries which might indicate the source of the problem).
Are there any files or registry keys which can be 'reset' to cause LU to go back to defaults?