Brian in Calgary just can't get the handles off of his faucets in the shower. He has tried to pull them off until his hands are raw. When he tried to pry them, he discovered that the plumbing in the wall is not stable and the pipes move forward. He tried WD-40 and CLR to get the handles to release. Then he broke a cheap tap puller and bought a better one, which didn't work either. Apparently his handles are just about welded into place. Unlike many plastic handles, Brian has cast iron handles on a brass stem which have really corroded together.
Since brute force obviously won't work for Brian, he needs to use something that will really dissolve the corrosion. WD-40 is a material designed to dry electrical wires, with a little lubricant added. What you need is a true rust and corrosion eater, like Releasall or Liquid Wrench. Now the problem is to get this material down into the matching grooves of the shaft and the handle. I suggest putting a little in the hole where the screw came out, and then lightly tap the side of the handle. The tap needs to be more like a vibration than a hammer trying to force anything. We need to vibrate the release solvent material into the grooves. Vibrate it for about 30 seconds. Let it sit for about 15 to 30 minutes. Turn the handle a quarter turn, add a little more solvent and vibrate it again. That will keep it wet, as it tries to evaporate off, and as it begins to loosen up, it will penetrate deeper until finally you get some real sidewise movement of the handle and it will wiggle right off.
It took years to freeze into place (you really should change the washers every year and you won't have this freezing problem), so be patient with dissolving the corrosion.
For information on mechanical aids for this task, check out Pullers.
For general information on changing washers, check out Tips.