Error 942: At least one of the variations associated with this listing must have a quantity greater than 0.

In order for a multi-variation listing to become/remain active, at least one of the variations must have a quantity greater than 0. Variation quantity is set through the Variation.Quantity field. The exception to this rule is if the seller's account is opted into the Out-of-stock feature. With this feature, the quantity of a single SKU listing and the quantity of all variations of a multiple SKU listing can be reduced to 0 and the listing will be kept alive, but the listing will be hidden from search until quantity is added to one or more SKUs/products.