Actually this has nothing to do with the roiter, I have tested this on 2 different routers, one old and one latest version/model.
I'm using the latest updated boot9strap on latest Luna on new 2ds XL with everything done correctly, there is a bug which makes the wifi disconnect and reconnect itself quite frequently, you just have to keep pressing test connection until it works or restart your 3DS and try again. Same problem with checking for updates