A few suggestions:
- Check to make sure the slide is closing completely. If the slide is stopping slightly out-of-battery (not quite fully closed), some of the hammer's energy will be redirected from the firing pin to closing the slide, leaving the light hit on the rim that you talked about. Load and release the slide, then (keeping it pointing safely downrange!) lean forward and look at the side of the slide and the size of any gap between the front face of the slide and the rear face of the barrel. Lean back to your normal shooting position, fire the shot, then lean forward again and see if the slide/barrel relationship looks any different. If there is any increase in the gap and then the weapon fails to fire the next shot, then the slide failing to close may be the problem. WHY it is failing to close completely may be difficult to determine, though.
- Check for any burrs on the rear edge of the chamber. If there are any sharp edges, gouges, or burrs on the rear face of the barrel at the chamber's edge, it might be snagging on the round as the slide closes, preventing the round from fully seating into the chamber. When you try to fire, some of the firing pin's energy is redirected to fully seating the round, and you get a light strike mark on the rim (because it wasn't well-supported by the edge of the chamber, and therefore the rim doesn't get crushed properly). You could try chambering a round, extracting it without shooting, then checking the sides of the case for scratching or gouging.
- Look in the extractor recess/cutout on the right side of the barrel (at the rear) and see if there is any build-up of crud in this area. If so, clean it out. Put a drop of oil/lube on the extractor plunger (behind the extractor in the slide), and work the extractor ever-so-slightly back-and-forth (not too far, or it may pop right out!), checking for free movement or any indications of binding. If the extractor is not moving freely in the slide, or is binding in the barrel slot when the slide closes, it may prevent the slide from closing completely, with the possible problems I have previously described, above.
Hope you get it figured out and corrected; I know how frustrating it can be. Especially with a fine, accurate piece like a Medalist!