What exactly happens when you change your 3DS region?

Solution 1:

I decided to test it. My usual profile settings are USA with no state set. Here are my results after changing my location (called 'Region' in the profile settings, which is confusing) to Argentina - Buenos Aires.

• I was still able to play downloaded titles. Shovel Knight worked fine, but I had to accept a basic terms of use agreement.
• I could not enter the eShop or Pokemon Bank, and they displayed a message saying that the region (location) had been changed, and that it had to be changed back to access those services.
• After changing my region back, I had to accept a terms of use agreement for downloaded Pokemon Bank, but not for Shovel Knight (Shrug)
• I was able to connect to any NNID services as though nothing had happened.
• The only thing I didn't try was creating a new NNID. I wasn't sure if I would have to delete the one I have now, but I know for certain that if you delete one you WILL lose all downloaded titles permanently.

Verdict: As long as you don't delete your NNID, you can change your location settings as much as you like, and you won't lose your downloaded titles, although you may not be able to use anything that requires your NNID to be logged in from your original location.