This seems strange... it sounds odd that you have to add the students again if you included them. When you restore the course make sure you include all user data, the Course users and the user files, like the image here (taken from http://docs.moodle.org/en/Restore#Restoring_a_course_from_the_site_files). If you do not tick the user data for the assignment or select Course users or course files the new course won't have the assignments associated to the students.
Let us know how you get on!
Cheers
Teresa
