The WordPress User Profile admin screen, edit made there will not affect entries in Connections. The Link extension is required for that. Is it installed? If so, what version? When it is installed, there will be a page in addition to the User Profile page there will be a Edit My Directory Entry profile page. It’s on that page the user should edit their entries. Unless the Form extension is installed then your users can edit their entry on the site’s frontend on the directory page.
Hopefully this helps a little. Let me know.