The reason behind it may be you have modified the table while defining the relationship between the tables such as change the null / not null property for the columns in the table. This will make the tables uneditable and convert the database in Readonly mode. To overcome this issue just close the diagram without saving it and refresh your database. Open the table structure, make the changes and then again open the daigram after refreshing the diagram.

This time the database daigram will allow you the editing. 🙂