You could try using a credit card. Also you could contact Nintendo and explain the issue. I had helped a person with the same issue and after they had tried using a different connection it worked for that person.
You could try disabling the wireless connection on the 2DS by simply tapping the wrench in the left top corner of the home menu. Let it be disabled for 5-10 mins and then activate it again. I hope this helps.
ALSO I FORGOT TO MENTION HAD YOU UPDATED THE SYSTEM TO THE LATEST VERSION? THAT MIGHT CAUSE THE ISSUE.