Try pulling it up, could be pushed down too hard, thats happened to me. Like others said you could not be used to it... are you talking about an Nintendo Controller just to clarify? Anyways, you can always switch out the joystick.
Done that many times with my PS4 controller. You can get like 5 sticks for 1 dollar on eBay. You open it up, recommend watching a video, I didn't but I can tell someone not too haha, and you pull it out and put a new one in, not as hard as it may look. Trust me :)