Symptoms
Unable to login to Designer and runtime site using Domain account after switch to Forms Authentication. Full message:-
Authentication with server failed : The method or operation is not implemented

Diagnoses
This issue is not happening when accessing the Designer and Runtime site within the server itself. Somehow this indicate that this is due to some server configuration.

Resolution
Local Security Policy "Access this computer from the network" rights not granted in App Server. This is a requirement for any IIS site utilizing IIS Authentication.