@hychu-chan- The nature is "fixed" but the personality is not.
@Ashinto- make sure to clear your old "cards" by trashing them, as if your card slots (you can hold only 3 at a time- downloads) if when you have 3, it will not allow you to do the download.
Example: you have Mew, Regigigas, and Raiku already downloaded. Your "cards" is full, so select the trash option to discard Mew and Regigigas, and you will be able to download Entie, and Suicune. Then your cards is full again, you will need to trash again for the next download.