The skill list is fixed, as per this pdf character sheet. Skills refresh between investigations, I believe, or perhaps between scenes. I don't recall which exactly.

Your fighting skills do the same, which means you lose the fight when you can no longer expend points to hit or shoot the other guy. One's Health score is the rating that lowers as you take physical damage, and one's Stability score is the rating that goes down as you take mental damage (from seeing unspeakable horror, for example).