I added a new ADO.Net Entity Data Model into my project and used the Update Wizard to add tables into the model. Five of the selected tables were added to the design surfac
One other solution is to ensure the account you are accessing the database via has some permissions to the table, Select at least. The table won't be added if the account has no permissions to it.
In SSMS under Security, right click the user or role, then Properties. Then click on Securables. The top table shows tables currently accessible. If the missing tables aren't there, click on search and find then, highlight them in the top table, then assign permissions in the lower table