Make sure that cookies are enabled in your browser.
Make sure that the CGIPath in mt.cfg corresponds to the URL you are using to access Movable Type.
If you login to MT at
http://example.com/mt/mt.cgi but your CGIPath is set to
http://www.example.com/mt/, then the cookie gets set for example.com.
But when MT redirects, it looks for the cookie to be set for www.example.com. (In most cases, it is always best to use www in both the CGIPath and the URL you use when accessing Movable Type in your browser, as this can avoid other problems such as with the posting of comments.)
Make sure the CGIPath includes the trailing slash (/).
If you still have a problem, set your browser to prompt you for a cookie when you login, and see if you get a prompt.
Are there any error or warning messages on your screen, in particular, referencing
pragma: nocache, or similar?