Varnish problem, user logged out for a HIT page
Maybe too late, but I had exactly the same problem, I spent two days looking for what is wrong, then I read in settings.php:


  Without "Vary:Cookie", authenticated users would also be served the
  anonymous page from the cache.


So change 'ommit_vary_cookies' from TRUE to FALSE in settings.php solved the problem.

$conf['omit_vary_cookie'] = FALSE;