RE: Is it the possible the connection between user account and Connections entry is broken/missing?
Sure… have those users logged in so their WP User account will be linked? If they have not, they need to login. The WP User account email and the Connections Entry MUST have a matching email address in order to be linked on login.
You can view which directory entries have been linked to which user on the Connections : Manage admin page. Look to the far right of an entry row. It display a Linked to label with a link to the WP User admin account profile page.
WP Users not linked to a Connections Entry will not have the “Edit Entry” link displayed. Instead they would have the Add Entry link assuming that user was giving the correct role capabilities.
Hope this helps, let me know.