Hi, I experience a similar thing to what you are describing. When watching a movie, playing a game or reading a book, I feel great at the beginning. Maybe itīs the thought of having most of it ahead of me, but when the end approaches i feel sad. So when iīm feeling bad i tend to watch incredibly long animes (those i know thereīs no way iīm gonna finish before my mood improves lol).
Itīs a natural thing, i think. However some people are more sensitive to it than others. Maybe the problem is that you develop some kind of emotional attachment to the characters in those stories, and the end of the story means this attachment will have to be broken.