It will normally take up to 20 minutes but it does depend on if eBay is 'busy'.
Important to note: When you finish blocking or zeroing out the products you want blocked or removed in the Inventory section, you have to push the changes to eBay by using the 'Upload to Marketplace' button on the dashboard.
Once the dashboard shows that the sync with eBay has completed and the Upload button is available again, check eBay to see if the listings have ended. or zeroed.