Theres a strange circumstance where if you get disconnected while using the PokeTransporter it locks you out for a little while, I think it is an hour. Pokemon Bank gives you a message when this happens, but PokeTransporter does not, so try waiting a bit and seeing if it fixes itself.
Also I wish my 3DS and games just knew when I was connected to the internet, instead of me having to manually tell Pokemon to connect every time. One day nintendo will have proper online functionality... Though it is definitely getting better. I cannot wait for the 4DS or whatever is next that won't have friend codes like Wii U.