When Rebirthing, any equipped items are un-equipped upon entering the game. Many of these items will be moved to the first open inventory space, or into an equipment bag.
However, exclusive items that are bound to your character will be moved into the "ME" Inventory Tab.
Check your "ME" Inventory Tab to locate your missing item.
Be sure to check your "Soul Stream Inventory" as of Mabinogi's Potential System Update! You can find this inventory space located in your Main Inventory window. Click the feather icon next to the "Shopping Cart" icon at the top right of your main inventory to open the Soul Stream Inventory, which acts as another inventory bag space for your items.