eBaymag lets you archive a listing. However, you don't delete it, but temporarily hide it from the list. So you have only actual listings on the Items page.
To archive listings, go to the Items page and tick them.
Then click the «Archive» button.
To access archived listings:
Click the Filter button
Then select Yes opposite to Archived
Click the "Apply filters" button.
Now you should see only archived listings in the list.
To withdraw a listing from the archive, you should tick it and then click the "Unarchive" button.
If you decide to delete a listing, you cannot restore it anymore.
To delete listings, go to the Items page and tick them.
Then click the «Delete» button.