Intermittent silent login failure
I believe this was due to the user logging in as http://example.com and then trying to access a link (from an email) to http://www.example.com/page-that-requires-a-login. In addition the user had a bad browser-memorized password for http://www.example.com, though his password for http://example.com was good. This apparently caused an odd loop of login failures.

I have uncommented the Drupal-supplied redirects in .htaccess that force all http://www.example.com URL's to redirect to http://example.com versions, and have told all my users they may need to re-memorize their passwords in the browser.