About your f***ing website.
meta.stackoverflow.com
meta.stackoverflow.com
A legitimate, helpful response (although it IS SO's login, so.... eh) that's a little bit of a "hey quit being a douche" is actually a pretty good way to go about it from a PR standpoint, in my opinion.
But hell at least they respond.
It feels like a gamble. You might win that user - or lose them badly, and reputation along with it.
I do occasionally find myself being automatically logged out for seemingly no reason at all but it only takes two clicks to log right back in.