I have seen this question asked before and answered as "That can't happen". but this has happened to me a couple times and i assumed i just couldn't find it. however it happened with my dawnbreaker and i was disarmed in the doorway of a room with a hallway behind me. i'm sorry i searched for quite awhile in the small area of the hallway as well as the room. there was nothing else that could have hidden it in any way and i used my torches and light spells to try to find it and there is no way i missed it. not to mention i have seen things disappear when i picked something else up or moved something so i can say for certain that things do disappear (in this case at least the name appeared as i moved over it).
It fell through the floor or ground mesh. I don't know who said "That can't happen," because it happens all the time.
Either reload a previous save, or use console commands (if on PC) to either walk through the floor or spawn in a replacement.
tclwill let you walk through things. Use it again to turn collision back on.
additem <item ID> <count>will give you an item. The item ID of Dawnbreaker is