You can password protect directories within your site from unauthorized users by using 'Web Protect'. This allows you to restrict material to only authorized users or store sensitive material online.
To password protect a directory:
Click on the Web Protect link under the Site Management header in Cpanel.
Navigate to the directory that you want to protect. Select a folder by clicking on the folder name link, or open a folder by clicking on the folder icon.
Click on the tick box next to the LOCK icon. (make sure you do this, this is something most people forget)
Enter the name that you want to appear in the Protected Resource Name field.
Click on the SAVE button.
Generally, you now need to add at least one authorized user to enable access to the directory. Refer to Adding an authorized user for more information.
When you check to make sure the password protect is working, please make sure you aren't just suffering from browser caching issues.