Theory 1: moisture
Were the leaves wet at all? I worked in a restaurant before, tending to the fridge. I had to make sure the salads were washed and thoroughly spun. Wet greens wilted and rotted faster and we had to toss them. The roots can be wet and exposed to water, but make sure the leaves stay dry.
Theory 2: freezer burn
This link mentions that cilantro can be damaged by freezing temperatures, which could be an explanation for what you're seeing? Is it so cold in your area that your refrigerator actually dips into freezing temps because the air around it does?
Meats can get freezer burn or taste off after freezing. One explanation I've read is that water freezes as sharp crystals in and around the cells. Upon defrosting, these sharp crystals can cut through cell membranes, causing cell contents to leak out and alter the meat structure. In theory the same could apply to anything organic.
Theory 3: dehydration
The link above and others I've read suggest storing cilantro as you do in the fridge, but covered with a plastic bag. Some wrap their cilantro in a paper towel. Either way, this creates an enclosed or somewhat-enclosed space that slows down moisture escaping from the leaves. The air in the fridge is generally dry and can suck moisture out of the leaves. I know this sounds like the opposite of too much moisture, but there's a window for how much moisture plants want--neither too little nor too much is desired.
I'd try to resolve this in the order above. If you left the leaves wet, I'd say that's a very likely culprit. I'd check your fridge temperature next: you could put an ice tray near where you put the cilantro to see if it freezes or starts freezing overnight. If it's still wilting fast, try doing what you did with a plastic or paper bag over the leaves--making sure the bag isn't crushing them.
Yes, oxygen (and sunlight) can affect the quality of oil. The oil turns rancid after some time. And storing the oil in a really airtight container (like a can from which air has been evacuated before sealing) should prevent or at least slow the process.
However, the problem is that you can't practically store your oil in an airless container and still use it. Yes, you can seal a bottle of oil. But there will still be air between the oil surface and the stopper, and the oxygen from this air will react with the oil molecules on the surface. And if you use a non-sealed bottle, the exactly same thing will happen. Unlike other cases (soda in a sealed vs. open bottle), the reaction of oil and oxygen isn't quick and aggressive enough to quickly exhaust the small amount of oxygen in a sealed bottle and stop. It will go on regardless of whether there is free air flow from the atmosphere or not.
So what can you do? You can still minimize the rate of rancidification. But it isn't the openness of the bottle that matters, it is the contact area size, because this is where the reaction takes place. Which means, store your oil in a (preferably tall and slim) bottle, as opposed to something like a jug. Protect it from light, because light is definitely damaging for oil. Also, buy it in small sizes, so you can go through it in a reasonably short time. And after all, don't worry too much about it. The reactions are slow, and the oils you use several times per week will not last long enough in your kitchen to deteriorate too much. It can become a problem if you collect special oils which are used seldom and contribute a significant part of the taste in a dish.
Best Answer
Freeze one, thaw it and see. The liquid separates out and leaves a pulpy structure behind. Tomato sauce (no chunks) thaws much better and separated liquid can be stirred back in well enough.
Canned works as we all know so no one is bothering trying to grow a freezer-friendly tomato, yet.