OLD PROBLEM: Closing your browser logs you off of any browser when using pssword authentication using .htaccess, which is what cPanel's password protect does. If you want to change users, close the browser ad try again.

NEW PROBLEM: Failing to login 5 or more times on a server bans your IP address. The server assumes you are a hacker trying to crack passwords if you fail to login so many times in a row. When this happens please open a support ticket and provide them with your IP address. Your IP can be obtained here:

http://glowhost.com/support/your.ip.php