Thanks for posting your question here.
If you relist your items from the Closed Listings page within your Auctiva account, using either the "Bulk Relist" or "Edit and Relist" options, those listings will be considered relisted items by eBay and will be treated as such with respect to search placement.
If you would prefer to repost your items as new listings, I recommend posting them anew from your Saved Listings page instead. Any listings you build through Auctiva are automatically retained for you on your Saved Listings page, so you should be able to locate the listings in question there unless you have deleted or saved over them.
I hope this helps. If you need any more specific assistance on this topic, please feel free to contact our Customer Support team directly from under the “Help” tab on our site.