Normally a pop-up stopper in a bathroom sink's drain will move up and down in the drain as you pull up and push down on the lift rod, which is located at the back of the sink's faucet. When the stopper will not move at all, one of the parts on the stopper's mechanism has either broken or come out of adjustment.
Inspect the Stopper
When the stopper will not lift up or down as you move the lift rod, try grabbing the top of the stopper and pulling it straight up and out of the sink's drain. On some sink stopper mechanisms, you must untwist the retaining nut on the side of the drain pipe and pull out the end of the pivot rod that feeds into the side of the pipe. With the stopper out of the drain, check it over for cracks or other damage. Pay close attention to the bottom of the stopper, if it has a small opening, since the opening is where the pivot rod contacts the stopper.
End of the Lift Rod
The end of the lift rod may have become disconnected from the clevis strap, under the sink, meaning no matter how much you move the lift rod up and down the stopper will stay stationary. When you look under the sink, you will see one end of the clevis strap that is shaped like a "C." The end of the lift rod is supposed to feed into the "C" shape's two holes, and a small set screw in the "C" holds the lift rod in place.
Inspect Pivot Rod
The pivot rod should be inserted through one of the holes in the other end of the clevis strap, with a spring clip holding the pivot rod inside the clevis strap. Damage to the pivot rod, such as cracks or bowing, will affect how the sink's stopper moves. You will need to drop the stopper back into the drain, with the opening in the stopper pointing toward the opening in the drain pipe before you can reinsert the pivot rod into the opening in the drain pipe and tighten the retaining nut.
Readjust the Mechanism
If the various parts of the stopper mechanism are intact and attached correctly, the stopper mechanism is out of adjustment. You need to pull the lift rod all the way up before you can readjust the mechanism. Loosening the set screw on the clevis strap slightly will allow the mechanism to settle into the right adjustment. After you wait two minutes for the mechanism to self adjust, tighten the set screw and then try working the stopper. If you still have problems, move the end of the pivot rod to a different hole in the clevis strap and readjust where the lift rod attaches to the clevis strap. You may need to go through some trial and error to find the right adjustment.