I've waited to post this possible bug, because it seems so unlikely. But I do have problems logging in and staying logged in. I input my e-mail and password; usually I get no error message, but I'm not logged in either (no change of userpic, still see the "sign in" button).
The only thing I've found that works - and this makes no sense to me - is logging in with a different browser than my most recent login. So I switch between safari and chrome.
This is not a great bug report, but there it is. It's been happening for at least... two months.