This is my headcanon about why Aslan had “left” Narnia during the Telmarine Age. After the Pevensies suddenly disappeared, Narnia was left without rulers. The disappeared Kings and Queens couldn’t be found so the Narnians finally decided to choose a King by themselves. Hatred and envy rised among them, what’s more, some murdered their compatriots as well, others killed their talking animal “enemies” for meal. All these were offenses against Aslan with two points:
only Aslan can appoint the new King for Narnia if the previous ruler has no heir,
murder others and eat talking animals were serious sins.
They broke the Laws, so Aslan decided to punish his people by leaving them but promised if they return to Him, He will return to them as well. This was the beginning of the Dark Age followed by the Telmarine Age. When Aslan felt that his people repented, fulfilling his promise he went to save them from Telmarine’s repression. Then, he made a covenant with Narnia (and King Caspian X) that he would not leave them without a king or queen ever. Aslan also knew that the Green Witch would rise one day and she would kidnap Prince Rilian. But Aslan had already made the plan before anything happened to bring Rilian back: he had chosen Eustace for this task to fulfill, he invited him to Narnia to work on him, so the boy became a dragon as it was not without purpose. Then, he invited him again along with Jill Pole to save Rilian, for the covenant not to be broken, and not let the past happen again.
Aslan takes care of Narnia -- like a father.