The serial number versions of Grapher save the registration information in the computer's registry. You must be logged in to the computer with Administrator rights to save information to the registry.
If you are not the Administrator, you can resolve this issue by right clicking over the Grapher shortcut or application and clicking Run as administrator. That will open Grapher in administrator mode. Select Skip registering and click Finish.
If you cannot save this information to the registry, then the program will prompt you to register the software each time you open it and an IT administrator will need to perform the above steps.
Updated July 2019