Around the time I added my Miiverse account to my new 3DS XL and purchased a few homescreen themes, I've been having problems with internet connectivity.
I would attempt to access the shop, only to have it be stuck in loading for up to 5-10 minutes before it gave me an error code (022-515), which I looked up to find that it was stating my router was having problems.
I rebooted my router and manually entered a DNS as opposed to auto-obtaining one, but it changed nothing (as it was connecting to the internet, just not the eshop)
I can connect to the Internet Browser, enter/register friend codes, use Colors! 3D's online gallery and connect to Pokemon Omega Ruby's functions, but Animal Crossing New Leaf's update screen and the E-shop don't seem to want to cooperate.
My system is completely up-to-date.
At the time of having these problems, I checked the network status and the E-shop was NOT down or having problems.
I also attempted to reboot my system each time I was prompted to when I got the error, which had no effect.