In order for the second chance offer to be able to work, eBay creates a "Buy It Now" listing for the buyer who receives the offer; the listing itself isn't searchable or able to be viewed by anyone other than yourself and the buyer it's offered to, and only they can purchase it. This listing has a duration equal to however long the offer is valid for (I believe they can be made available for up to 48 hours, but you have to choose how long to make it available for at the time you send the offer).

You can end a second chance offer early or let it expire on its own, then you'll be able to relist it for general viewing / purchasing etc.