Stem Rot on Squashes. Take good care of your squash plants to avoid stem rot. The term squash includes both winter squash and summer squash. Summer squashes are usually eaten while immature, such as zucchini, while winter squashes are eaten when mature, such as acorn squash. These plants are frost tender and grow as annuals in most climates. Squashes are fairly easy to grow, but a few pests, fungi and bacteria problems that can cause rotting of the stem.