Are you using third party nunchuks? Those tend to break/not work as well. Make sure when you buy any Nintendo accessory it has the little golden seal of approval usually on the front or back. That goes for the Wii Remote as well. Also, make sure you are using standard alkaline batteries.
I have not heard a problem like this before, but most likely it's a problem with your console doing something to the nunchuk. You can call Nintendo at 1-800-255-3700 and see what can be done. Additionally, if a repair is needed, if you bought your system within the last year it will most likely be free. 