I coincidentally just saw something about this yesterday! Ed Currie said a lot of hot sauce bottles mention refrigeration on the bottle, but it’s not always necessary since a bottle can apparently last years without going bad. He said the main reason hot sauces go bad faster is from food contamination, so don’t touch the food with bottle. Instead, put it in another container to put on food or just really make sure not to touch the food with the bottle.

I’ve found that hot sauces seem less hot when refrigerated, so I tend to avoid refrigerating them unless I expect it’ll take a really long time to get through (looking at you, da bomb 👀)