Hello!
First, restart your browser and try again.
Second,open cpanel >> Password Protect Directories
Do you see any "locked" icon against the folders that you have password protected ?
If not(and also for rechecking), click that folder.
You will see
Set permissions for "YOUR FOLDER".
1.SET CHECK MARK for "Password protect this directory"
2.Type some name for the protected directory.
3.Add an user.
Third(if it is still not working) - Manual method:
open/create .htaccess in your password protected directory.
---------
AuthType Basic
AuthName "Password Protected Folder Name"
AuthUserFile "/home/CPANEL_USERNAME/.htpasswds/YOUR_PWD_PROTECTED_FOLDER/passwd"
require valid-user
-----------
It should now prompt for Username/Password.
#I'm not going to comment on passwd file.
Write back if you have any problem setting up this!