You may have a corrupted "ProAppSystemID" file or Aperture cannot write to the System Library.
To stop Aperture asking for the serial number, first check, if you still have an old file "ProAppSystemID" in your System Library.
- Quit Aperture.
- Go to your MacintoshHD and open the folder "Library", then "Application Support", then "ProApps".
- Remove the File "ProAppsSystemID" to the Desktop, if it exist and restart Aperture.
- Reenter your serial number, hopefully for the last time.
Sometimes Aperture writes this file to a temporary directory, when it cannot write to the Library. If the above does not work, look at the temporary directory /tmp
Use the Finder's "Go" menu
Go > Got to folder and enter /tmp into the textfield. If you see the file there, move it to its proper location.
In this case you may want to repair the permissions on your system drive; you can do this using the "First Aid" tools in "Disk Utility" (located in Applications > Utilities)
I have the same issue. Followed your instructions, removed the ProAppSystem ID file to the Trash.
However i did not find the /temp file. Repaired permissions also.
What happens now is that once I enter the serial number, quit Aperture and open it again, this time it does make the request. But when I restart the computer the first time I open Aperture the request pops up.