Nondurability is a characteristic of not lasting long before falling apart or being used up. The nondurability of your new shoes is evident if their soles wear out after only a month.
You could construct a beautiful suit out of paper, carefully stitching it together, but its nondurability would quickly become an issue, especially if you wore it during a rain storm. Many things have the quality of nondurability because they're meant to be used up: in contrast to the durability of a house or a piece of granite, the nondurability of cupcakes or toothpaste is obvious. Nondurability adds non-, "not," to durability, from the Latin durabilis, "permanent."