Chicken and dumplings can typically last for 3 to 4 days when stored properly in the refrigerator. It is important to refrigerate the dish promptly, within 2 hours of cooking, and store it in an airtight container to maintain its freshness and prevent bacterial growth. If you're unsure about the quality or safety of the leftovers, it's always best to use your judgment and discard them if they appear or smell off.