Condiments, such as sauces and salad dressings, can keep indefinitely, as long as they show no sign of mold. Most are high in acidity, making the risk of bacteria growth very low.
Most condiments will keep their best quality if they are refrigerated after opening, although that often is simply a matter of taste and how we use the product. You don’t have to refrigerate ketchup, for instance, but most of us prefer it cold, so it’s convenient to keep it there.
You should always refrigerate things that call for it on the label.
— Kathleen Purvis