When I turn on my Wii, and I press any button on any controller, it connects properly.
If I press a button on any other controller, any other controller which was already connected loses connection, and the recently turned on controller never connects. After this I can connect controllers only after a restart.
I got to connect another controller but just after entering a game and selecting multiplayer. Otherwise it will just disconnect the already connected controller and I would have turn off and on again to be able to connect again.