There are successful books and movies that do something along these lines --Roots and Full Metal Jacket come to mind --so it certainly can be done, and done well. Memoirs and autobiographical fiction often do this as well. It's true to life that people may be an important part of your life "only for a season."
With that said, fiction is NOT reality, and part of the author's job is to impose a narrative structure that serves the reader. With that in mind, why not go non-linear? Ursula LeGuin's The Dispossessed interweaves two parallel narratives, one of the protagonist's early life and young adulthood on his home planet, and one of his exile in later life on a nearby planet. Although the two worlds are almost wholly separate, the characters in each stay alive in the reader's interest because of the structure. You could do this either directly and structurally, as she does, or through flashbacks, memories, dreams, allusions, and so forth.
I'm actually planning something similar in my current writing project. The protagonist's father dies at the very start of the primary narrative. But his relationship with the protagonist continues to evolve throughout the story, first through memories, later, through new information and stories the protagonist learns, and eventually, through the protagonist gaining a new internal understanding of his father.