That´s banning you.
Do not access MiiVerse via 3DS.
I´ve been play online with public headers for months, and never had banned.
The 3DS stores information about games that you played, and when you connect to MiiVerse it is transfered for Nintendo.
I tried to explain that to the forum members...
Try to put the sky in console with the blue button pressed. then, remove and reinsert (without pressing button now) 3 times and see if it works.
Good luck!
If you are saying deleting games from mSD and putting back, then you need, in diskwriter, click with right button on the game, and backup save data. And when you put the game back in mSD, right click on the game and restore save data.
Keep the Bold that i point of original template from sky3ds.
Change only the "this line" that i point.
I always do this way, and never get 002-0123 error.