This is what it says in the Beta Manual:
Condition and Repair of Equipment
Through the natural course of use, all equipment-weapons, armor, and tools alike-will suffer from deterioration and a decline in effectiveness. At the hands of a skilled crafter, however, such equipment can be restored to prime condition.
- Do-It-Yourself Repairs
First, ensure that the proper tool is equipped. From the main menu, access the Item List and then Inventory. Choose the item you wish to restore, then click the Repair button to initiate the process.
- Enlisting the Aid of Other Adventurers
From the main menu, access the Item List and then Inventory. Choose the item you wish to restore, then click the Seek Repair button to initiate the process. You may choose to offer a certain amount of gil or an item as payment for the repair.
- Emergency Repairs
Certain NPCs located in city-states can perform emergency equipment repairs upon request. Be warned, however, that the subsequent quality of equipment repaired in this manner will fall short of those worked upon by honest-to-goodness crafters.
*To repair equipment, you will need to have the necessary materials for the item to be repaired.
By using appropriate, high quality materials, you may be able to cut down on the materials used.
Which just leads me to believe that the system is broken since I couldn't click the "Seek Repairs" button at all.