You will lose access to the additional retainers, starting with the most recently added retainer. The list is arranged by date, with the oldest retainer on top. This means the retainer at the bottom of the list will be the first retainer to become inactive. You can view this from the Sort Retainers Menu in-game.
FAQ Article: 70139
FAQ Category: [Service Fee] [Official Website] / FAQ Sub-category: [Options] [Mog Station]