it's true that antioxidants will break down over time once you open it to the air. but they do have preservatives that help stabilize them to prevent that breakdown. if you start to see the color change of those products that's a sign that they are breaking down. keeping the jar closed tightly or keeping it in the refrigerator will help somewhat but i often find that when i keep something in the refrigerator i am too tired or lazy at the end of the day to go get it from there so i don't end up using it and then it does no good at all. so if you are very motivated and you will go to the refrigerator every time you want to use it that's fine. but chances are you will use that product up before it breaks down if you are using it enough so you don't have to worry about it.
i read that open jar packaging oxidizes the anti-aging ingredients in moisturizers. will it last longer in the fridge?