Growing Zucchini

Can one of you experienced gardeners tell me why all of the longer stems that run along the ground from my zucchini plants (i.e., those that are longer and extend out from the main plant to form new leaves)are turning brown and stringy looking? It is almost like these longer stems are rotting on the ground. Too much water? Too little water? Fungus? So far we have only put water and fertilizer on them. We live in Wilmington, NC, and the soil here is sandy and has a pH near 7.
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