Do you have all your 3DS ports open or perhaps your 3DS under DMZ mode? I am starting to think something in the ports is causing me issues but.... heh, the modem my ISP gave me is a piece of shit Thomson 782. What a goddamned nightmare.
I don't think the router is always to blame, maybe ISP traffic shaping/priorization or connection quality has something to say too. I've always rocked piece-of-shit ISP routers (including a Thomson right now) since the first time I got ADSL/cable and never EVER got a problem connecting Nintendo consoles to the internet with default settings, everything auto, no fiddling in router settings.
Edit: one thing: check if your router has some kind of firewall enabled and disable it. Will help with other devices connection to the internet too.