In order for the module to synchronize products with zero quantity on eBay (without closing them), the following conditions must be met:

• The option “Enable Out of Stock mode” must be set to “YES” in the module’s general settings
• The option “Use Out of Stock option” must be enabled on eBay in your seller account (My eBay => Account Settings / Account Preferences)

This will ensure that products with quantity 0 are included in the “Update out-of-stock products” list (Sync tab) that the module will specifically create once these options are activated.
Please note that for a product with 0 quantity to be updated and not closed, it must be active on the site.
A product with 0 quantity but deactivated will always be considered to be closed regardless of the Out of Stock option.

Notes:

• Products with 0 quantity will not appear in the general list “Update synchronized products”, unless you set the value “Ignore products below this minimum quantity” to 0 in the module’s general options (General tab > General)
• The module includes a feature that allows excluding from the “Update out-of-stock products” list those products with 0 quantity that have already been updated to that quantity. This is intended to optimize bulk or cron-based synchronizations.