If you have been trading mail with Cid, good. When you receive his fifth reply, he tells you that his wife was scared by a monster that has taken up residence in his basement. Its time for the heroes to investigate! Go to Cid's house in Canaan and fight this dastardly creature.
I've been trading mail with Cid and Takka for awhile now, and neither of them will reply anymore when I sent mail, yet I haven't received Cid's reply about there being something in the basement of his home.

Do I have to complete a specific part of the game before this will take place, or do I simply have to continue mailing him until he finally responds?