This is an interesting question, because it seems to infer that Mitty does change. I actually don't think there is any evidence to suggest this in this brilliant short story at all. In fact, from start to finish, we are shown a man who remains exactly the same, and we see no development in his character.
The only ostensible change we could point to is the way that Mitty leaps from different daydream to different daydream, however, it is important to realise that he does this as an escape from the monotony of his existence, his terrible wife, and his own weak character. The dramatic transformations that occur in his character are just elaborate fantasies that allow Mitty to be the man that he is not able to be in reality. Let us consider for one moment his last daydream:
He put his shoulders back and his heels together. "To hell with the handkerchief," said Walter Mitty scornfully. He took one last drag on his digarette and snapped it away. Then, with the faint, fleeting smile playing about his lips, he faced the firing squad; erect and motionless, proud and disdainful, Walter Mitty the Undefeated, inscrutable to the last.
This ending is rather humorous on the one hand, because it presents death as being a preferable alternative to living with Mrs. Mitty. However, on the other hand, it could also be considered tragic, as it shows that Mitty lacks the courage and bravery to resolve his problems in real life. The repeated fantasies that he embarks upon only serve to show the way in which he has not actually changed at all.