This occurs because the user doesn't have the permissions necessary to edit a field on the constituent record.  In order to copy the value, security group permissions will need to be altered to allow editing. 
  1. In The Raiser's Edge, click on Admin in the main menu.
  2. Click on Security
  3. Under Groups, double click on the group name to open its details.
  4. Under Group Privileges highlight Records and click the Options button.
  5. Locate the field that needs to be changed and verify that the Edit checkbox is marked. 

Note: If only one person needs access to do this, a new security group will need to be created for that user.  The user will need to log out of RE completely (File > Exit and Sign Out) before the new security settings take effect.