If you want that I cross check your settings on your environemnt, the only solution that I see is that you order the billable support at
www.jms2win.com/en/joomla-multisite?page...35&category_id=1
Otherwise, verify again, step by step that when you login, you have a call with "login" and not logout.
If you have a "logout", this mean that you are not logged in joomla.
Verify that with the "Joomla Login".
Perhaps you are using another module to login in joomla and that in fact you are not logged. (I don't know).