I too have this same problem.
Funny thing is that I have another blog on the same host set up the exactly same way (from what I can tell) and it works fine.
I have tried all the suggested fixs etc to no avail except I have found that it has something to do with Zone Alarm. When ZA is turned off it seems to work OK, when ZA is on it keeps going back to the login screen even though it is the right password.I have tried adding it to trusted sites etc under the 'Privacy' tab and allowing all the options etc.
Also have tried this both with Explorer and Firefox.
One interesting thing is that if you click in the address bar of the browser (after you have attempted to login once or twice) and then hit GO or Return you can enter the blog OK. But when you want to go to another page you have to go through the same process...click in address bar and go etc..
P.S As I was writing this I figured out one way to get it to work (with ZA). Under the Firewall tab select Zones then add your site there as a trusted site/host. This seems to work.
Funny thing is that my other blog doesn't need this.