I just received my refurbished 3DS console yesterday, since I was having issues with my L button.
I was pretty happy with it, until I realized streetpass function didn't work anymore (My friend lent me his 3DS for Puzzle Swap and Find Mii).
I tried to read about that problem on forums, a lot seemed to have the same issue after that their datas were transfered to another 3DS console. I didn't find any solution though. Trying to turn off/turn on 3DS and the wireless bouton, delete each other Mii on Mii Plaza, checking if I hadn't block by mistake the other user on each console, nothing worked.
Has that happened to you when you upgrade to 3DS XL for example?
I'll wait a little and probably will call back Nintendo customer service ...