Immidiately after the last firmware update in October I'm suffering the same problem with laptop with Windows 7 Home Basic. It asks login and password before connecting to MBL Public Share. Though I have only to enter any letter (not default admin) in login section and computer connects. No password is required.
All my other network devices - laptop with Windows 8 Pro (updated during this time to Windows 8.1), Dune HD mediaplayer, Marantz M-CR603 network player, Philips Smart TV are connecting to MBL Public automatically.
I have tried all advices and recipes sugested in this thread. Nothing helps.
It seems to me this is some incompatibility of the latest firmware with Windows 7 Home Basic.
Before this firmware update I've never faced any problems with my MBL (2TB) for the last 2 years I am using it, updating firrmware regularly.