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As AndyC points out, the real issue might be that the sights are off. That can be checked fairly easily by another experienced shooter. If it seems the sights aren't really off, the issue probably comes back to something the shooter is doing while trying to get the shot off.

Trigger manipulation is the bane of practically all pistol shooters. Ideally, once your finger contacts the trigger, you add pressure STRAIGHT BACK on the trigger until the sear breaks -- all the while maintaining a perfect sight picture. Simple in concept, but difficult in execution. As others have mentioned dry fire practice (absolutely dry -- gun double or triple-checked to be empty and no ammo in the room) can help tremendously.

Starting with an empty gun, set the sear (cock the gun); get a good sight picture on a specific target; move your finger to the trigger and begin to add pressure while watching the front sight; continue adding pressure until the sear breaks while you are watching the front sight. If your grip is changing or your trigger finger is making the gun move you should be able to see the movement of your front sight as you do this. Repeat this process 30 - 100 times a day for a while, trying to eliminate all disturbances to that perfect sight picture as you move the trigger.

Also remember that we need to practice correct mechanics again and again to ingrain them. The easiest way to see movement is to go slow at first and strive to get the movement correct ~99% of the time. Then and only then incrementally step up the pace. You can't really expect to be able to be perfect at slow fire and then pop off a rapid fire string that is equally perfect unless you've ingrained the correct movements both slow and fast. Don't even try fast until slow works as you want it to.

When you are again shooting live ammunition, you may discover that your shots are again drifting in a particular direction from your intended point of aim. This may be your body's personal response to the sound/recoil of the firearm. You may want to have a shooting buddy prep your gun between shots, randomly providing you with an empty chamber. If you are paying attention to the front sight all the way through the trigger press, you'll likely notice the flinch in anticipation of the shot going off when nothing is in the chamber. Again, dry fire practice is called for to make the proper trigger press the one your mental pathways produce by default.