I have perfectly fine internet yet when I try pokemon bank I get error codes 006-0520 and 006-0501. My internet works perfectly and can connect to any other online app. Nintendo needs to get its act together. We have been waiting over a month and they have still failed to make pokemon bank work. Its pathetic.
My Pokemon Bank works perfectly fine. Keep trying and you may get through. I blame the sheer amount of people trying to sync their NNID with the app. You may have better luck after midnight, when most people are in bed.