The phrase "one's rare appearances" means that someone doesn't appear or show up very often. It implies that the person is seen or witnessed on only a few occasions. Full definition
More recently, egg salad sandwiches make rare appearances, despite the fact that it's a childhood favorite. (kitchenconfidante.com)
But in spite of my best efforts, it only made rare appearances, sliced - thinly, on an occasional cookie plate downstairs in the restaurant. (davidlebovitz.com)
But it's the relatively rare appearances at RC of working scientists, often only identifiable to us onlookers because one of the principals clearly knows who they are or mentions their work, that I find most helpful sources of real understanding and interesting new information. (realclimate.org)