This is an issue that has occurred several times to me. Each time has been with Chrome on a subdomain multisite setup. Which is annoying because Chrome is my preferred browser for development.
Using Chrome, or potentially any browser, on a wp multisite install with more than one subdomain blog set up, the user is constantly redirected to the login screen despite entering valid login details. A good indication that this is the problem is that clearing the browser cookies cache allows an unaffected login. Not really a long term solution.
The solution is pretty easy as it happens. Simply place the following in the wp-config.php file before the line which reads
/* That's all, stop editing! Happy blogging. */.