Friendships are vital to our health and well-being. Researchers at Michigan State University analyzed responses from over 270,000 people in nearly 100 countries and concluded that as we age, friendships are more influential than family ties in their effect on our health and happiness. Other studies have found that our immune systems and longevity benefit from strong social ties. And yet we don’t have anything like a user manual for something so important—and fragile. Bonds forged over decades can easily fracture and even shatter, turning BFFs into strangers. Then, like a distant relative, an old friend can reappear, hoping to become part of your life again.

Whether and how to rekindle a friendship is a knotty issue. It’s harder to form friendships as we get older; science also te...