Refrigerated. Store your potato soup in an airtight container in the refrigerator for 3-4 days. Reheat in a saucepan over medium heat. You can also add a splash of cream if the soup thickened.   Don't freeze it. I do not recommend freezing this soup. The potatoes have a tendency to be grainy after being frozen, and the texture won't be as nice. If you already frozen your soup, I would defrost it in the refrigerator, then reheat it in a saucepan over medium-low heat. Then add a small amount of cream and use an immersion blender or a standard blender to try and bring the texture back as much as possible.