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I lost my Altair's sword in a battle and then accidentally picked up another weapon trying to retrieve it. But then it sheathed that dumb weapon and I wasn't able to exchange. Since the game autosaves I reset the XBOX. But do you know if you lose a weapon does it just go back to the rack in your villa and you don't really lose it?
Except for that one point, you can't lose your weapon in battle. Altair's Sword looks a lot like the common swords the guards sometimes carry so that might be it. You don't sheath the weapons you pick up.