There are very few stories without a character arc. The change may be huge: take, for example, William Munny's change from reformed outlaw back into outlaw in Unforgiven. Or Michael Corleone's birth as a gangster in The Godfather. Or the Narrator's pugilistic transformation in Fight Club. Part of any good story, after all, is watching the effects events have on the protagonist.
In this well-observed and sensitive video essay, Kevin Rogers uses Mike Nichols' The Graduate, one of the best-loved films of the twentieth century, as a model for ideal character development:
Rogers employs an interesting diagram to make his point—one which might be helpful to aspiring filmmakers and storytellers of all stripes. If we view a character as an apple at one end of a seesaw, the goal for any good story should be to move the apple to the middle of the seesaw, so that it slides down to the other side, reversing the conditions observed at the beginning of the film. The force that moves the apple to the middle of the seesaw is the catalyst of the story—the element which drives narrative change—and that is what Rogers is most interested in here.
If you're trying to develop a story that seems to be flagging in its development, The Graduate might be a good film to rewatch.
When we meet Benjamin Braddock (Dustin Hoffman) at the beginning of The Graduate, he is a recent Ivy graduate, a naif, a character upon whom external forces act, rather than the other way around. When he meets the seductive Mrs. Robinson (Joanne Bancroft) early in the film, the event is fortuitous in a couple of ways. First, it speeds up his sexual maturation. Second, and more importantly, it intensifies and amplifies the tremendous pressure Braddock feels from all sides—to justify his education, to find a good job, to focus his life. This pressure, Rogers argues, is the catalyst needed to help Braddock grow up, so that by the end of the film, rather than waiting for good things to happen to him, he might take the initiative to charge into his girlfriend's wedding and shape his life, finally, in a way that matches his desires.
If you're trying to develop a story that seems to be flagging in its development, The Graduate might be a good film to rewatch. It raises crucial questions: Who is your protagonist at the outset? How do you want that protagonist to change by the end of the film? How might you go about making that change? What pressures might cause that change to happen? These could be changes from within the character's mind, from external social structures, or from elements of the plot, such as character conflict.
The key consideration, as you do this planning, is the end result: When you take a good look at the character at the film's conclusion, who—or what—do you want to see staring back at you? It's entirely your choice.