J.J. Abrams directed Star Wars: The Force Awakens, and is directing Episode IX. Why did he skip this one?
Was it his choice (like he had a conflict)?
Or did he and Disney have a temporary falling-out?
He only planned on directing one. He took over when Collin Trevarrow was fired and presumably asked again.
Rollingstone Magazine - December 6, 2017
J.J. Abrams couldn't resist returning for Episode IX, out in 2019. "I had no intention to return," says Abrams, who directed 2015's The Force Awakens. "But when the opportunity presented itself to finish a story that we had begun with these new characters, to tell the last chapter of their story, it felt like there was a chance to do it in a way where we could go beyond, and do better than we did in Seven. I learned so much in that movie and I saw that this was a chance to sort of realize something that we hadn't quite achieved – and part of that was it was simply the beginning of these new characters and their story. The opportunity to sort of take what we had learned, to take the feeling of who these characters are and what they are and give them a final chapter that felt in the spirit of what we begun? It was too delicious of an opportunity to pass up."
Note: Even when Kathleen Kennedy approached him the first time for The Force Awakens, he turned it down, but eventually when she asked again, and after Abram's wife helped convince him, he accepted. Almost all of Bad Robot's early works reference and allude to Star Wars & many are generational family sagas with metaphysics (Alias, LOST, Fringe, Alcatraz, Revolution) with other genres blended in.
There is no indication that they had any kind of falling out at this time. And it was announced early on that there would 3 different directors for this trilogy. He also served as an Executive Producer on The Last Jedi. However, there was some kind of disagreement that occured after/during LOST, as Bad Robot switched distributors from Buena Vista to Warner Brothers Television and no Bad Robot television series has ever aired on a Disney-owned channel since.