As long as the slab is airtight, I can't imagine that any further oxidation or other type of age based deterioration would occur.
As I understand it, only BVG slabs provide any protection against UV rays, so I wouldn't store them in any direct sunlight.
As for humidity, I'm not sure. Some people have claimed that a PSA label can wrinkle if the slab is stored in humid conditions. Does the same hold true for the card? I thought all slabs were supposed to be airtight?
I also own at least one SGC slab whose label has become yellowish/brownish in color (stained, if you will). Still legible, but noticeably darker in color than my other SGC labels. My gut tells me it's due to something like cigarette smoke emanating from the card, but who knows? The card itself looks fine to me.