Since then, I've frequently had the log-in page come up when I wanted to post a message, although I clicked "remember me on this computer" the first, the second, the third, etc., time.
I don't always have to log in again; only about every second time.
Is there anything I can do to make the "remember me" stick?
Eloise, try clearing your temporary internet files too. That worked for me when I had the same problem.
Internet Explorer Version 6 Series - Temporary Internet Files > Tools > Internet Options > General Tab > Temporary Internet Files - - click "Delete Files". This may take several minutes. (Do not delete cookies here, see next step.)