Some ideas/questions to help you
1) What is the brand/model of monitor (I may have better info based on it) For example, I have had to adjust additional things in a Wells-Garndner 46xx series when the horizontal width didn't work right.
2) Is it the horizontal Hold, Position or Width you're adjusting? Hold is sometimes a small rectangular square adjustable coil mounted on the circuit board, Position is usually a standard potentiometer pointed out the back, and width is a taller open coil with long rod mounted on the circuit board or to the frame.
The reason I ask what it is, is that only the potentiometer one can be turned with a metal object. If you're trying to turn a coil (either in the silver can or in the large open shaft one) then using a metal device, like a screwdriver (can) or a hex allen wrench (open coil) then the metal in the tool will affect the tuning of the control and as soon as you move the metal from the control it will produce a different result.
If this is the case, use a nylon or plastic device. Bob Roberts sells a pack of 4 that offer both blade ends and hex shafts.
TV Tuner cleaner will only help if it is a potentiometer (plastic end you turn with your thumb or screwdriver). It will not help coils
3) You may need a new cap kit and/or other components replaced, but start with the cap kit if the above info doesn't help.