So if A Christmas Story is based on a series of vignettes of childhood, then why weren't there more movies that explored other aspects of Shepherd's childhood? Well, actually, there have been sequels, they've just had the misfortune to be mediocre follow-ups to a movie that is shown around the clock during Christmas season.
It Runs In The Family (originally entitled My Summer Story) was intended as a direct sequel to the original, even though it was filmed almost 11 years later, necessitating new actors for almost the entire cast (except, oddly enough, for Ralphie's teacher Miss Shields). Still, the presence of returning director Bob Clark and the benefit of using the same source material meant the sequel wasn't too bad, all things considered. As to why it never caught on the way the original did, audiences may have been too put-off by the new cast, or maybe comedic stylings had changed too much in the ensuing decade between releases.
That movie sequel, however, fared better critically than the direct sequel to the original released in 2012, A Christmas Story 2, which aged Ralphie up to a teenager. Unlike the original and It Runs In The Family, it wasn't based on Shepherd's writing, and it received a critical thrashing, so maybe it's better not to think about it.