Aron believes that he needs to be there for Ren when he finally returns to reality because it would break his heart if Ren disappears again without telling him what happened. So that's why he continues to stay.
Just like Ren had always done for him. And he wants to keep his promise to him… Because he doesn't think that he will ever lose that trust, that devotion.
…
[After The Night]
The three of them didn't waste any time and kept on going. They had traveled further than usual to avoid being seen and followed, they had gone over several obstacles just to make sure that their presence isn't detectable.
Since Aron did share some information with Riku, about the premonition that the place would be overrun by demons or hiding to ambush incoming knights that wanted to scout the area. And that's why they rather keep a low profile as they don't want the demons to notice them.
