Whenever a Personal Shopper marks an item as out of stock, the website places that item into the Unpublish queue, but it does not unpublish it right away.
Instead, there is a delay which we call the "grace period" - by default your grace period would 1 full day, but you are welcome to reach out to us if you would like to adjust it.
Let's take the default example of a 1-day grace period - here is how the process would look like in this case:
Today: a Personal Shopper marks an item "out of stock" and the item goes into the Unpublish queue.
Tomorrow: the website checks if the item has sold in the store again, or the sales of the item ceased on the same day that it was marked "out of stock". Then, overnight, the website either keeps the item published if it started selling again in the store or unpublishes it if the item stopped selling.
This rule only applies to items in regular categories that are set up to publish and unpublish automatically - what we call the "Automatic Mode" categories. If you mark an item from a "Manual Mode" category as out of stock, it will not be unpublished - the idea is that such categories should be controlled manually and just because a Personal Shopper excludes such an item from an order, does not necessarily mean that it's completely out of stock and most likely the item will be available again later today or tomorrow.
The "Manual Mode" of operation is usually advised for categories such as Fresh Fish, Fresh Meat, Sushi, and Takeout - basically, any category that needs to display a fixed menu/selection of items online at all times. Whenever you discontinue an item from such a category, you would simply unpublish it manually and it will stay offline.