Yup there's weirdness going on - On Chrome with Windows 7 I'm having trouble with staying logged in.
I just signed in, it seemed to be going well, then the page came up again looking like the login hadn't been successful. There was no error message--just showed me as not logged in. However, when I hit the Today's Posts link, the posts from today came up fine and the page showed me as logged in.
I'm experiencing this as well.
I have someone looking into this today and sorry for the hassle.