Sticking is usually caused by one of a couple of reasons. The most common with controllers is debris (usually food getting lodged into the controller. A quick look around the surround should prove to find if the controller has this problem in general. If there are no signs of this then it is unlikely there is any inside.
The second and probably more terminal problem is that the return spring for the stick has become broken, maligned or similar. If this is the case then really the only way to repair it is either recalibration or replacement. Failing that a new controller is probably required. However I have had success in the past with getting the controller undone and then gently lifting the outer plastics a bit and then refitting the screws.