I believe I have solved this issue. I can't fix the plugin, but I have a workaround.
Here's what I found.....
When you go into the plugin settings and fill in your login/password info, or change the options and click the apply button, it saves to the audioscrobbler.ini file located here:
C:\Documents and Settings\Administrator\Application Data\J River\Media Center 11\Library\audioscrobbler.ini
Now, I noticed that when starting up MC and pulling up the plugin settings again, the login/password is of course blank now. Turns out it was attempting to read, and not finding, the audioscrobbler.ini file because it was looking for it here:
E:\Documents and Settings\Administrator\Application Data\J River\Media Center 11\audioscrobbler.ini. (note the lack of the Library folder in the path).
So, here's the fix. Substitute your own paths.
Go into MC and edit the audioscrobbler plugin settings.
Fill in your login info. Click the login and apply buttons.
Leave MC as is....
Using windows explorer, find your audioscrobbler.ini file in a path similar to above, in the Library folder.
Copy that audioscrobbler.ini down one level to the Media Center 11 folder and save it there.
Now close MC and restart.
Check to see if the login info is still there.
High-five me if it works.
Please test and report your results.