In the story of The Catcher in the Rye by JD Salinger, why did Holden and Jane stop seeing each other?

They never really went together in the first place, did they? They were just neighbors about a year and a half earlier and played checkers together. Holden clearly has fond memories of her and sees her as a kind of ideal girl, but that seems to be as far as things ever went. Evidently they stopped playing checkers together because one family or the other moved.