Typically, that happened if you put the CE effect on an identical item, such as putting a CE bound shield on an actual shield or enchanting your boots with CE Bound boots. However, the CE bound item effect uses relatively few enchantment points, so it can easily fit on a number of items. As long as the CE bound effect doesn't clash with the enchanted item that creates it, there shouldn't be a problem, provided that you "repair" your equipment by taking off the CE enchanted item and re-equipping it. Using the armorer skill to repair bound items is a Bad Idea?
I just tested it, and the moment I removed the CE item, the bound items disappeared. I didn't even need to drop it back into my inventory. I had clicked on it, held the mouse button, and moved it off my character and *bam* all my bound items disappeared. When I moved the mouse back over my character and let go of the button, the ring was re-equipped, and the moment I closed the inventory window, all my bound items were re-created.