According to Square Enix, if you do not log in for online play for over three months, it's possible that the game's server will delete your character data. (No doubt, this is to keep from overworking servers, so in that regard, it might make sense.)
If you do not want to shell out for a DQ X online subscription, you can play online for a few hours each day during a predetermined "kid's time". You don't have to be a kid to play during this free period as there's nothing that checks your age. You do need to log in at least once every three months if you want to keep your character data.
利用券を購入せずに時間がたっても、また再開できますか？ [Square Enix]