It's punishment for deleting your cookie. Don't sign in we don't want that. Just stay signed in. Trust us.
I was able to directly link this page however, which I bookmarked:
I don’t understand the problem, if people want to try or sign-up for your service they’ll locate the signup button. That’s a one time problem. A hidden login button just annoys existing customers.
My feeling is that this is down to testing without privacy in mind. Your site might be fine, but others aren’t so a minority of users will clear cookies at the end of each browser session. That’s not a senario most will test for or experience.