The Remember me feature is a neat feature to save you from logging in everytime.
But in case you could'nt get your browser to 'Remember you', this could be one of the reasons: Your browser's cookie settings.
Go to Tools > Options > Privacy > and have "Remove Cookies on close" disabled or Cookies enabled - whatever the option is.
The login credentials for your particular browser are saved in your cookies and they should be enabled.
Tim Davis found and shared, this tech solution with us when he encountered this problem in IE and Firefox.