When you go to a 'new' anvil and put in one slot a used enchanted(chest-plate), and in the other slot a new (chest-plate), and at the bottom it says the amount of levels needed (And you do have enough) - After you accept the trade your levels are used like normal and you get the 'new enchanted (chest-plate)' ...

However, after a few seconds of putting it in your inventory the (chest-plates) both (unused enchanted, and new (chest-plate)) fall back to the ground, deletes your 'new enchanted (chest-plate)', and keeps your levels - making you have to re-log back in to obtain your levels back .

I tried making a video on this - at the link below:

http://s1236.beta.photobucket.com/user/Caleb_Ferguson/media/Anvil%20Problems/Untitled44.mp4.html