Now, I can't use the admin area.
This is what happens: I enter the admin username + password and get into the admin menu (which lists some links, eg. "Easy Admin", "General Settings" etc.). Now, when I choose one of these links, I am redirected to the login panel again!
If I enter a wrong password, everything is as it should be (i.e. I get an error message even before I see the admin menu).