We assume that all products set to ‘do not track inventory for this product’ in Bigcommerce have an inventory of 10 so that the product will list.

If you have products using this setting that you don’t want to list on eBay then you should block the products under the Inventory section in our system. See the FAQ: Can I block an item from listing on eBay?

If you are using this setting as its a product that you have a lot of inventory for then you might be better to put an actual number of inventory against the product in Bigcommerce so that the product does not de-list then re-list again.