How do you unarchive an item on eBay?

Yes you can. Go to the top right of the Ebay page and mouse over "My Ebay".

On the drop down list, click on "Purchase History". When it takes you to the next page, under "Purchases" tick on "Archive".

Next to an item's "more actions", click on that and on the drop down list, click "move to recent purchases"

The item should go back to your purchase history.