As explained by the Snow Priestess, the Thousand Year Frost Tree is a "vessel" of the land that accumulates the energy needed to keep the giant barrier around the Yuki-Onna's village active. By doing this, the tree has protected the village since "Ancient Times".
However, when Fairy Tale invaded the village, they planted an Egg in the roots of the tree. The ivy-like tentacles around it have grown so deep that the Yuki-Onna cannot remove it without risk of destroying the tree itself. The reason that the barrier around the village is weakening is because the egg is absorbing the tree's energy.