The Relic Quests are a great example of poor game design

[Ultimatecalibur]

In order to upgrade the weapon, the game removes it from your inventory and replaces it with a new one. If you are equipped with it, you are then not equipped with any weapon. The game does not allow you to not have a weapon equipped. Based on what I have observed, that is the reason this happens.

The problem is more that the current turn in step requires that you be in the correct class/job which requires that you be equipped with an appropriate weapon/tool so that you can turn in your relic for upgrade.

The first two steps of the Skysteel/Dragonsung tools had you exchange them at a shop which you could do as any class/job. This was a lot less aggravating.