Only situations with a published figure are listed. A blank isn't “forever” — it means no reliable number is published for it.
Storage
Store at: Pantry unopened; refrigerate at 40°F (4°C) or below after opening
Refrigerate after opening: Yes — refrigerate at 40°F (4°C) or below
Tip: USDA FoodKeeper: 1 year in the pantry unopened, about 4 months refrigerated after opening. Refrigeration ensures that commercial sauces and condiments stay fresh for a longer period of time. Shelf-stable commercial barbecue sauce is safe when stored at room temperature after opening. Quality, not safety, is the reason the labels on these products suggest that they be refrigerated after opening.
How to tell if Barbecue sauce has gone bad
Mold
Off or fermented smell
Fizzing or bubbling
Color darkening
These are the general spoilage signs for condiments & sauces — never taste something to test it. When in doubt, throw it out.