All servers for the old gamed Soul Silver, Heart Gold, Platinum, etc have gone down to work on White, Black, White 2, Black 2, so the servers won't come back.
The servers keep you connected on wi-fi, but when it is down, it no longer allows access to wi-fi. As long as there is one down, you cannot connect, but if all are up, then you can connect.
It stays up for about a month after a new generation of Pokemon comes out, but then it collapses. This is because the server has moved on to the newer game. So, you have no access to wi-fi in your game now.
So no matter what you try, you cannot connect to wifi in your game unless if you play one of the mentioned.