The reason you sometimes can't 'Save and add another' or 'Save and close' when adding a new site is because either something was invalid, or the system made a change and is making you aware of it. More than likely what is happening is that you entered a project but left 'allow direct activities' unchecked. The system automatically sets allow direct activities to true if there is a project entered, and then it reloads the form so you can make any other changes, or uncheck it, if desired. There is also an info message at the top right explaining this when it happens.