You've Been Storing Celery Wrong Your Whole Life
It seems like celery, which has such a pleasant and crunchy snap when it's fresh, can wilt in just hours. However, similar to asparagus, which you can also grant an extended shelf life if you store it a little differently than you're used to, you can make sure that your celery maintains its crunch after you put it in the fridge with one simple maneuver.
Although it's tempting to just put your celery in the fridge in the plastic bag in which it was sold, this is part of the reason your celery is wilting so quickly. Similar to how putting an unripe piece of fruit in a paper bag causes it to ripen (via SF Gate), the sealed plastic bag in which the celery is packaged traps the ethylene that the vegetable naturally produces, which speeds up the ripening process.
The trick to preventing this occurrence is to use a different type of substance to wrap your celery: aluminum foil (via Food52).
The secret ingredient for extending the life of your celery
Though it seems like it's just as impenetrable as plastic, the aluminum foil can actually allow the ethylene to escape, which prevents the celery from decaying. If you store whole heads of celery tightly wrapped in aluminum in tin foil, you can actually keep it fresh for anywhere from two weeks to a whole month. It does require a bit of a balancing act though because you want to wrap the aluminum foil loose enough that it allows the ethylene to escape but tight enough that it keeps the moisture in. It might require a couple of tries to get it right, and one trick is to not seal or crimp the edges. Of course, aluminum foil has fallen out of favor lately because it's not the most environmentally friendly product, but if you can reuse it to wrap a few rounds of celery, you needn't feel too bad since you're reusing it.