The short answer to what makes Macomber's life short but happy is: Well, it wasn't. It was short because he died young but it was not happy. Hemingway is employing verbal irony in a story with situational irony to underscore his view of the story The Short but Happy Life of Frances Macomber, which was derived from an actual incident that occurred in Kenya. Hemingway is also employing a formerly common cliche used when a person suffered the misfortune of dying young: "Well, s/he had a short but happy life."
The verbal irony in the title is revealed when you get to the conclusion of the story and ask, as you have done, "Why short but happy?" Frances Macomber had a stable marriage because Margo was so beautiful that he would never bear to divorce her and because Frances was so rich that she would never bear to leave all his money. In this ironically trite and greedy stability, Margot took liberties with fidelity and freely practiced infidelity, which she once again enjoyed with the safari guide Robert Wilson the night following Macomber's fearful run from the wounded and charging lion, an action for which she was utterly ashamed of him.
In the end, Macomber finds a new bravado and daring in the face of his wife's infidelity, seen in the face of Robert Wilson. This new bravura steadies him in his encounters with the buffalo and he has great success in that hunt. Robert Wilson sees the change in Macomber and is pleased and admiring even though he knows that Macomber now will not endure Margot's infidelity. Margot sees the change in her husband and perceives a threat--undoubtedly she also knows that her infidelities will no longer be permitted and suspects that her beauty will no longer provide protection from being divorced from his money. She undoubtedly feels that Macomber is on the verge of raining on her parade, as the saying goes (i.e., stopping her fun and making her miserable). When Macomber is facing the third, wounded buffalo, he fires and fires but the buffalo isn't downed. The reader expects that Robert Wilson will fire to at last kill the buffalo and save Macomber from the outcome of the wild charge. There is a shot fired. Ironically, it is fired by Margot and lands with expert precision of aim in the back of Frances's head. Wilson believes, as do we, that Margot intentionally killed her husband.
Again, the title presents a verbal irony (something said or written that contradicts what is or what is expected to be) that represents the situational irony (a situation that contradicts what was expected) of the story's end: We do not expect Margot to be driven by her husband's new bravado to kill him. Following a final reiteration that Hemingway chose to use of a once common cliche in his title, we arrive once again at the conclusion that Macomber's life, although short, was not happy: Hemingway is metaphorically ironically shaking his head at the irony of the story of Mr. and Mrs. Frances Macomber (Macomber sounds a bit like "somber," as in a somber tale, doesn't it?).
I don't agree with the previous answer on what makes Francis' life short and happy. The answer is simple. It's only when he found truth in courage and manhood for a short time that he was truly happy. Hemingway's most noble character trait is courage in the face of death. To Hemingway, masculinity, in its purest sense, is the ability to become fearless and strong in a gravely dangerous situation. Prior to Francis assuming this characteristic, which evolved slowly on the hunts subsequent to his humiliation with the lion, he was miserable. He was anxious, cuckolded by his wife and resented by Wilson, a man he revered for his courage. Slowly, over the span of the story (which only spans several days if that), Francis finds his courage, eschews the oppressive dominance of his wife and as such finds true happiness. Thus, the time from which the realization overtakes him to the time of his death is short, albeit happy. Prior to the realization and the demonstration of his manhood, he led an unhappy (longer) life.