Either there are no more presents available at this time, or you do not have sufficient Internet connection.
If you received a present within the last month or so, there is a big chance that you will not get another one for a little while.
First things first, your Cure Rhythm avatar is adorable.
For the OP...
I read somewhere that Nintendo stopped at-home downloads for North America and Europe. I can't get presents either without going to a Nintendo Zone, which I never do.