The XA has an electromagnet release. When the camera is wound, an armature is moved to be held against the two poles of a permanent magnet. When the release button is pressed, a coil around the magnet is energized, creating a magnetic field in opposition to the permanent magnet, causing it to release the armature.
In your case, there may be debris between the two poles of the magnet and the armature, so that the shutter fires at the end of each wind cycle.
If you remove the bottom cover of the camera and look just behind the lens, you may be able to see the armature moving each time you wind the camera. Snip a narrow slip of sturdy paper (say 1/16th inch wide) and a couple of inches long and, with the camera set so it has just released, interpose this slip of paper into the camera between the armature and magnet poles. S-l-o-w-l-y wind the thumb wheel one or two clicks so that the armature just begins to press against the poles. Drop one drop of pure alcohol onto the paper so that it wicks down into the camera. GENTLY try to tug the paper out, but try not to tear it. If you can't remove the paper, complete the wind cycle and try again -- when the armature begins to move, wind just one or two more clicks and tug the paper out, wiping off the face of the armature and poles. Now gently blow in a little air to evaporate the solvent, and maybe, just maybe, you'll have a working camera again.