The scientific reason? Not without seeing your specimen. (wink, wink)
Seriously, unlike cut flowers and other herbs like sage or rosemary, parsley is simply not happy in water for more than a couple of days, especially towards the end of the growing season and/or if it had been harvested some time ago. Nothing to do with the water, although that should be cold and changed daily for the best results.
Your parsley simply stopped taking up water and started to shut down cells, starting at the bottom of the stem. They are drying out and shrinking, so can no longer support the stem and appear to be wilting. This will continue up the stem once the water stored in the cells starts to evaporate. Conserving water already present is the most you can do. The plastic bag, which is slowing down transpiration, helps. You are lucky it is not starting to rot or develop moulds in the humid atmosphere inside an unventilated bag at room temperature.
If you have no fridge, try hanging a bunch of parsley upside down in a plastic bag in the coldest place you can find and out of direct sunshine. To save wastage, chop and freeze is the only way to go for long-term storage, or buy potted parsley instead of bunches, if you have no garden or balcony for growing it yourself. Some stores and farmers markets sell parsley with roots or parts thereof still intact. They will keep in a jar of water far more successfully.