If you relist an item on eBay, it will be relisted with a new item ID generated by eBay. Therefore, you will have to manually add this item again to HGR. 

When a listing ends on eBay, it will also show as terminated on HGR and will not count against your subscription limit. If you search by its ID, you can still see it on HGR for reference, but when your search results return more than 1 item, terminated items are not displayed (you can still see them using the advanced filter).