Because archaeologists call them storage pits, we have assumed that the traits we associate with storage are occurring. In modern usage the connotation of storage is not for a very short term followed by the complete removal of all items to another location. We should not be fooled by the words we use to describe prehistoric cultural activities. I suspect that the few formal artifacts, sherds, and pieces of debitage found in these features were introduced from surface middens or living floors when the pits were first dug or as they slumped when abandoned. Although re-using abandoned storage pits for refuse or in food processing is practical, new storage pits must be dug to store the newly processed food.
Pits gradually become unusable due to vermin, insects, and mold.
The food supply is too important not to expend a little effort to dig new storage pits in the very sandy soil. The last items to be deposited into the refuse pits would be the expended, non-repairable, broken, and heavy processing implements. Intensive processing has been completed for the year. The processed foods they will carry to the winter camp weigh enough without someone wanting to bring their favorite muller, milling stone, hammerstone, or shaft straightener. The river banks and fields are filled with appropriate replacements which can be easily obtained when the need arises.