Most products are not significantly affected by exposure to air assuming you're not leaving it open continuously or in a over heated car, for example.  The one exception is antioxidants which do start to "oxidize" and deteriorate somewhat when exposed to oxygen in the air.  You'll notice that most  companies that make Vitamin C serums package them in dark glass stoppered bottles.   But yes, you will lose some potency over time with these - just how much is open to debate.  The companies say very little and others disagree.   I think the industry is moving toward "closed" packaging for most antioxidants and I think we'll see  more of this packaging for just this reason.

In the meantime, I think we should all just use common sense.  If I open a bottle of the SkinCeuticals C & E Ferrulic, I don't keep it around longer than about 2-3 months. I store it in a drawer and  close it right away after I use it.   Dr. I