On the blog http://revamann.wordpress.com we have a similar problem, except that it only seems to apply to one user, so the issue isn't the particular theme or the formatting of the link.
There are two Administrators. When we are both logged in, I can see the Edit link under each post on the blog page, and can click on it in order to edit the post. The other Administrator cannot see the Edit link, even though she is recorded as the Author of the post (I put it up originally, but then changed Author to her name). She says that she also cannot see the blue bar above the site that contains the My Account, My Dashboard, etc. options. However, she can go in via http://revamann.wordpress.com/wp-admin/ and edit the post.
Has anyone encountered anything like this before? I would be grateful for any help.