You should use Kies 3 to backup all files, especially Story albums, to your PC. The following operations will delete all your albums in your S4.
After backup, you can go to applications manager–all–story albums, try to clear cache. Then try again.
If story album still does not work, you have to try to clear cache and clear data for story album. It should work now, but all your old story albums will be deleted as well. So, backup, backup first.