Probably you try to access your site without www and it redirects to the www site, e.g. you access http://example.com/administrator and it redirects you to http://www.example.com/administrator or vice versa. The same applies for http:// versus https:// protocol. The same applies if your site is known by two or more different domain names and you're not using the canonical one, meaning you get a redirection. Remember that the browser thinks of each of these URLs to your site as a different authentication domain, therefore will ask you for username and password.
The solution is to always access your site with its canonical URL, i.e. the one you see on your browser's address bar when you see the Joomla login page.
Nicholas K. Dionysopoulos
Lead Developer and Director
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