I don't know whether this helps or not, but I have continued to use the original URL
and have found myself always automatically logged in, but whenever I've used the "newer" URL
the automatic login doesn't work. Consequently I keep using the older/original URL that works. I wonder whether the problem has something to do with the shift from "www.test" to "www." in the URL doesn't have something to do with the problem.
οὔτοι ἀπ’ ἀρχῆς πάντα θεοὶ θνητοῖς ὑπέδειξαν,
ἀλλὰ χρόνῳ ζητέοντες ἐφευρίσκουσιν ἄμεινον. (Xenophanes, Fragment 16)
Carl W. Conrad
Department of Classics, Washington University (Retired)