Windows Experience Index has a log file "%SystemRoot%\Performance\WinSAT\winsat.log". That may give some relevant details.
I had the same error message and, in my case, the log file reported "Unable to save". It appears to have been Kaspersky Internet Security 2010 which was blocking WEI from saving the results. The complete WEI test ran OK and even flashed-up the 'completed' message but this was then immediately replaced with the "assessment could not be completed" message ... because it could not *save* the results.
Can I suggest you try another AV package? If you disconnect the network cable you could safely uninstall your existing AV package and see if WEI works again. If that resolves it, perhaps you need a different AV package from now on.
Personally, I found that Microsoft Security Essentials appears to not have this issue and I can now get my rating again. But I may try some other (try before you buy) packages to see what's best.
Worth a try?
Keith.