One of the biggest contributors to wilting and aging in vegetables (especially leafy greens) is loss of moisture. The air in your refrigerator tends to be very dry so higher moisture things like Kale, Spinach, or Lettuce are best stored in high moisture places like a Crisper/Vegetable bin.  If your refrigerator is not equipped with a  crisper/vegetable bin then we recommend that you use a plastic bag or container with some holes or opening to minimize the moisture loss and wilting (just make sure that they have a slight opening in them so the activated oxygen will get in the bag).

You can also use a wet paper towel, sponge, or mist to add moisture.