Purée persimmons and sugar together in a blender, then cook mixture in a nonreactive saucepan over medium heat, stirring constantly, for about 2 minutes. Add water slowly, continuing to stir, and cook for 3 to 4 minutes longer. Remove mixture from heat and allow to cool to room temperature. Refrigerate, covered, for at least 3 hours.
Remove mixture from refrigerator. Beat egg whites unt