When you talk to a moogle you can save, use a tent, access mognet, or in some cases buy treasure. So if you access mognet and the moogle dosen't give you a letter try to check your walkthrough. I know some moogles don't give letters, but thats only a few.

Is it possible to miss the whole mognet quest? I know in the begining of the game you talk to a moogle about it but I don't know if you can miss out on it or not. Could be a glitch.

Anyways try talking to the moogle several times. If it fails you can either start a new game or continue and hope you can deliver it later.

This just crossed my mind, I think you can only have three letters at a time. So best thing to do is deliver the letters you have (if any).