I believe we've found a bug here... my friend is playing through my copy of FFX, and had the same problem - Rikku's sigil disappeared from the inventory after being acquired. The game disc is in perfect working order, no scratches or dirt - and it's the same problem that Jessweeee♪ has described.
It didn't happen to me, but then again I've only done the Celestial Weapon side-quests once. It seems entirely likely that the disappearing Mercury Sigil is a randomly recurring glitch.