The stems have separated from the roots or the roots have gone black.

Water Sprite is a floating fern, which means it only has a very small or weak root system. These often get delivered without or damaged roots due to being potted. You usually leave it float in the water for a while for the roots to develop, and then you can anchor it down or plant it. Water sprite receives a majority of its nutrients out of the water column, so does not need roots to feed.