Tommy Lovins loves cooking and even built his deck with his grill in mind. He bought a Kenmore grill about 3 1/2 ago, but he said that about a year ago, the big grease tray started rusting out on it.

Kenmore has been a household name in America for well over a century. It’s one of the nation’s top producers of refrigerators, dishwashers, laundry machines and other home appliances. But what happens ...