Lolita_Nocturna I'm not sure about what you have going on with having to introduce yourself to the Sage again other than if you waited too long to go back. Unless your sim has the Beloved trait from completing the Friend of the World aspiration, friendship and romance levels will deteriorate over time until they reach the point that the relationship is culled from the panel.
As far as learning from the Sages: If you have already learned everything that a Sage can teach you for the Magic rank your sim is at, then they won't teach you anything and you'll get a wall post saying essentially that. Once you gain enough magic perk points to advance to the next rank, then they will teach you something new if you haven't learned everything for that level by reading the tomes or gotten it already by practicing.
Hope this helps.