To draw from D&D's deeper roots, recall Narsil, an ostensibly magical sword, which was broken (unintentionally, mind you, but still) and later reforged into a new sword with much the same powers. That's not an uncommon motif amongst magic swords and their heroes in Norse mythology.
In fact in Order of the Stick strips
#297 and
#298, Roy has his broken magical sword reforged into a new more powerful magical sword, as well.
Now, I don't have a problem with the idea that the material is magical, and the shape has nothing inherent to do withthe magic. Just as a sword can be melted down and reforged into a new sword -- or an axe-head, or a helmet, or gauntlets for that matter -- a magical enchantment could feasibly be "melted down" (disenchanted into residuum), and "reforged" (re-enchanted) into a new item.
The only stipulation I may add here, if the rulebook hasn't already, is that the old magic is tied to the old material, so whatever you create from the "residuum" must be an item made of the same base material. In other words, if you disenchant a magic ring, you can make another ring, or a magic necklace, or a magic brooch, or something else made of gold and silver and gems... But you couldn't use the residuum of a magic ring to make a magic cloak, or magic boots, or a magic shield.