Did you migrate from a clone or TM backup?
Then you may have copied an old ProAppsSystemID file.
Be sure to enter the serial number, when you are logged in from an account with Administrator priveleges - otherwise can it not be stored.
Aperture is installed for all users on your mac, so the serial number is written to the system library, not the user library, and this requires read/write access for administrators. Do you enter your serial number using an administrator account?
To stop Aperture asking for the serial number, first check, if you still have an old file "ProAppsSystemID" 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 ProAppsSystemID to its proper location in /Library/Application Support/ProApps .