Copying from another comment of mine:

Not too concerned about the logout, as we do that fairly frequently anyway (by which I mean probably twice in the last six months)

The bigger concern is people who use a password manager or rely on their browser to save their password.

Since you now login via another domain, the password manager won't have anything.

You can surely still recover your password, but there's far too many combinations of browsers and password managers to try to provide any help.