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Relationships and the love that comes from them are an important theme in the Hunger Games. Love proves to be integral towards keeping Katniss alive. She survived the difficult times following her father's death because she had Prim to look after. Her love for her sister (and her mother, though less explicitly) is what helps her to stay strong as a provider for the family. Likewise, Peeta's act of kindness with the bread, which she credits as having given her strength in that period, was dictated by his love for her, though she didn't know that at the time.
Further, her growing love for Peeta in the arena continually helps her. The most obvious way is by encouraging Haymitch to send her sponsor gifts. Though she claims she expresses affection only for the sake of the gifts, it can easily be argued that her true feelings for him are what help her survive the final phases of the Games.