Lee Angel makes jewelry for American Eagle and Banana Republic. You might want to contact them and see if they made these and whether they have a replacement pair available. Their website is easy to find using Google. Good luck.
That design reminds me of the John Hardy "Kawung" collection... I could not find an image of hoop-style although they did make them, but here are sterling silver drop style ones from the collection to give you an idea (I found an image through google):
http://www.myjewelrytrends.com/2010/03/john-hardy-kawung-silver-drop-earrings.html
You kick butt!! Those look close and are nice. That's the back up plan for right now.
Lee Angel makes jewelry for American Eagle and Banana Republic. You might want to contact them and see if they made these and whether they have a replacement pair available. Their website is easy to find using Google. Good luck.
The best thing about John Hardy is - if she loves them as much as the missing one - the company has a policy where they will remake an earring to match the missing John Hardy one.