Yes, I know there have been quite a few posts on here about this but I haven't really found one similar to my problem.
On Monday I could connect perfectly fine to the Global Terminal to trade and battle etc etc, but today when I've tried to connect it simply keeps saying it can't find an access point. I'm connected to the internet fine on my 3DS and everything seems to be working great apart from on Pokémon, which although it acknowledges I have a connection on the C-Gear doesn't seem to want to connect to the Global Terminal or to Game Sync.
It usually uses my 3DS internet setup without any trouble at all, I've never set up a DS internet connection on it because Black doesn't need it.
I am unsure to if this will solve your problem, but:
Step 1: Make sure that your 3DS Internet works.
Step 2: Though you say you won't need it, it might help out. Go to your DS Internet Settings (since your using a 3ds, black itself won't allow you. Try using another WiFi game that uses the DS Internet, like MKDS)
Step 3: With the DS Internet, add the router you are using for your 3DS Internet.
Step 4: If this, and other suggestions don't work, I'd reccomend contacting Nintendo.