I'm sure someone around this forum knows the technical specs on just about every aspect of the Wii.
I think lots of people have had similar problems, but it eventually works, could be a down server from nintendo.
As far as the antenna, all I'm saying is give my suggestion about putting the router near the Wii a try. Could it be possible your bandwidth could be reduced by a weak signal? I don't know but I don't think so. Do you have WEP? If you do then you are already sure that you are connected to your router. If not, could you accidentally be on another network? I don't know if any of this will help you but just give it a shot.