Silver and gold keys delete themselves from inventory and never drop again.
I accepted the quest, killed the first few naga, found the golden key. It immediately deleted itself from my bags. I then spent time killing ~60 more naga in hopes it would drop again. No drop. I then killed makrura for the silver key. Found the silver key on the 3rd kill. The silver key then deleted itself from my inventory. I then spent time killing ~25 makrura before giving up.
I am running no addons that maintain my inventory, no addons that delete anything. As far as I’m aware, the API as of 2.5.1 no longer allows addons to delete items anyway, so that rules that possibility out.