Overview
Whether an eBay listing stays active or ends automatically when it hits 0 quantity is controlled by an eBay account-level setting, not by 3Dsellers. This is called "Listings stay active when you're out of stock" in eBay's Selling Preferences.
If this eBay setting is ON, your fixed-price (GTC) listings will remain live on eBay even when the quantity drops to 0 - they'll just show as "Out of stock" to buyers until you restock.
If this eBay setting is OFF, eBay will automatically end the listing once it reaches 0 quantity.
Since this is an eBay account preference, 3Dsellers reflects whatever eBay does with the listing - we can't override this behavior from our side.
How to check or change this setting on eBay
Go to eBay's Selling Preferences page (My eBay → Account → Selling Preferences).
Find the Multi-quantity listings section.
Check the "Listings stay active when you're out of stock" toggle.
Turn it on or off depending on what you want to happen, then click Submit.
You can read more about this directly from eBay here.
Why this matters
If you're seeing a listing unexpectedly end when it runs out of stock, or noticing a listing stay live with 0 quantity longer than expected, this eBay setting is usually the reason - it's worth checking here first before assuming it's a 3Dsellers sync issue.
Related: if you want to control the quantity eBay displays independently of your real stock, see What is Inventory Control?