On your way through Esto Gaza to Mount Gulug, delivering a letter to Mogrika the moogle causes her to indicate that Mognet is shutting down because of an accident. From this point on, most of the moogles will not have any letters to deliver and won't ask you to deliver any due to problems at the home office, Mognet Central.
You can reach Mognet Central with a light-blue chocobo (REEF chocobo) on Disc 3. On the east side of this island, you can find a crack in the mountain. Feed Choco a Dead Pepper to make him open the crack, revealing Mognet Central.
Inside, the moogle Artemicion confesses that he used too much of a certain "thing" to make his fur glossy, and there wasn't enough left to use on the machine that keeps Mognet running. Leave Mognet Central and travel south to Alexandria. Then speak to Kupo at the bell tower ruins, and he'll give you a letter to Atla. Thus begins a chain of letters that MUST be delivered from moogle to moogle in order to revive the Mognet. Although the moogles tell you which moogle to deliver to, they don't mention where that moogle is located!
Atla is the moogle at Burmecia. Return there now and deliver the letter. Atla wants you to take a letter to Mogryo, the moogle standing outside the chocobo farm at the Black Mage Village. Mogryo has a letter for Kumool. Return to Ipsen's Castle and exchange letters with Kumool in the courtyard. You receive a letter for Mois, the moogle from the Ice Cavern, in return.
However, the Ice Cavern is now blocked by roots that have grown over each entrance. Mois has moved to Qu's Marsh on the Mist Continent, and now stands outside the former entrance to Fossil Roo. Make sure you have Quina in your party, or else you won't have access to Fossil Roo. Mois has a letter for Noggy, the moogle at Daguerreo. Noggy, in turn, sends you back to Kupo in Alexandria with a final letter.
When Kupo reads the letter, you'll notice that it says someone in Alexandria has the item needed. Kupo isn't any help, but we'll save you the trouble!
Talk to Ruby in the Alexandria Mini-Theater, and she immediately hands over some of her hair gel, otherwise known as Superslick. Return to Mognet Central and turn over the item to Artemicion. The Mognet gets back to business, and you receive a Protect Ring for helping restore Mognet.
Each time you deliver a letter during this sequence, the moogles give you Kupo Nuts if you don't already have one in your Key Items inventory. Return to the moogle family at Gizamaluke's Grotto each time you get one, and exchange each Kupo Nut for an item. By the time you're through, there should be four or five new little moogles running around!