So I had this problem occurring on several wordpress sites I was maintaining. I would access the admin login, enter the username and password, the site appeared to accept them, but instead of directing me to the dashboard, redirected me back to the login page. It would often take 2-3 login attempts before it finally “caught” and i was able to access the dashboard.
I did a bit of googling and determined it has something to do with the plugins (although I have no idea what exactly) Anyhow, eventually I found a tiny snippet which finally fixed the problem. Add the following line to the bottom of the first group of definitions of your wp-config.php file.
/*added to try and fix login loop*/
WordPress Admin Login works like a charm now.