My friend actually has a similar issue; She was able to log in once, then the next time she ran osu!, it's perpetually failing.
She's using Windows 7 Home Premium Edition.
I've guided her through opening all necessary ports in her Firewall/Adding osu! to her Allowed list and ensured it's running in XP Compatibility mode. She's using an Administrator account, too, so uhh...
Well I've just fixed it. I don't know if this was how but my password had none alphanumeric characters in it so I altered it so it only had alphanumeric characters in it and it then logged me in straight away.