Sorry to bump a fairly old thread but, since it still remains relevant to me, I thought I would.
I'm fairly sure the problem lies with the wireless channels - every time I disconnect I get the error code "91010". I think it has something to do with how the Hub actively changes channel in order to find the best one, a piece of technology the Wii obviously can't keep up with.
But, out of interest, while connected I decided to switch the channel and, interestingly enough, I immediately disconnected with the same error code - 91010. It would seem to me (purely from this) that even though we can manually set the channel, the Hub still changes the channel, and everytime it does, WiFi disconnects. This is just a theory and I know I have barely any evidence to support it, just thought I'd throw the idea out there.
If anyone finds a fix to this (by the way the one above didn't work for me, sadly), then please share it with us!!