Do you have one remote? Or do you have several and they all have the same problem?
If it's one remote, then the problem is probably with the controller itself. Getting a new controller should fix the problem.
If it's the same issue with several remotes, get one new remote anyway to make sure the problem isn't the controllers. If the same issue occurs, then it's more than likely your Wii is broken.
A Wii no longer under warranty can still be sent to Nintendo to be repaired: You just have to pay for the repairs instead of it being free. It'll run you about $70-$80, but it'll more than likely fix your problem.