I've researched this and found lots of people with the same issue and no answer, so I'll also post what I've done.
This is a *fresh* install of WordPress 3.4.2 at this service provider. When I go to Dashboard > Appearance > Themes and attempt to Save & Publish, it prompts me for my wordpress username and password. I input those and receive the message that I am now logged in. The updated preview displays and *immediately* returns to Your session has expired. Please log-in again.
>I am using the Twenty Eleven theme. Same error with other themes.
>I had only one plug-in running (Jetpack) and I've disable it. *NO* plugins are running.
>I have twice uninstalled and removed EVERY WordPress file from my root directory.
>I've had my ISP delete my account and set it up again with a fresh install of WordPress.
>I have WordPress running properly with this ISP on 2 other accounts.
>Subdomains for WordPress Address and Site Address are exactly the same.
>I've cleared the browser cache/history.
I've seen the answer give to this question that this is a wordpress.com issue rather than a wordpress.org issue. WordPress.com insists that server side installs is wordpress.org.
These are all the suggestions I've seen so far, but none have worked. Any other ideas?