I operate two websites in a narrow niche. When I do an advanced search on Google for a rare keyword that both of my sites are optimized for (e.g. orange tallit), the site that has almost no backlinks and poor onsite optimization shows up several times in the results, whereas the website I've put all my resources into and that normally does quite well doesn't show up at all. What's going on? Does that mean a lot of U.S. web users are not going to find me at all? Could it be because my main site is not registered in the U.S.? How much traffic am I missing out on?
You gave yourself the answer - Rare Keyword - sometimes by having a low competition keyword in a domain name or all over the site you don't have to anything to get ranked.