Order placed and order shipped emails only go out when the option is checked in their user profile. You may want to make sure the user's email address is correct. Go to Company / Users and search for user's name in the search bar. Then proceed to the email distribution section at the bottom of the page. Ensure the option for orders placed and orders shipped are checked.
If the user requirement is to receive all order placed and all order shipped emails from all their portal end users, check the option Email Distribution under their user profile.