Can confirm a similar case with Pokémon Black Version 2 (USA) on retail using a Nintendo DSi.
Long story short, despite having configured the connection settings to connect to 164.132.44.106, the game throws error 20110. This has been tested on both secured and unsecured protocols using the home router, a NETGEAR Gateway C6300 DOCSIS Cable Modem (only capable of unprotected and WPA encryption types). I've even attempted erasing the WFC data, to no avail.
...Two things that baffle me: It refused the connection even on an unsecured line, and a friend of mine confirms he can connect using a router of similar security encryptions.. which leads me to believe it's a router-based issue.
Any insight on this is welcome.