Star Wars has proven that Palpatine should have stopped Darth Vader from turning against him in Return of the Jedi. The third film in the original Star Wars trilogy ends with Vader protecting his son, Luke Skywalker, by throwing Palpatine into the Death Star II's reactor. While Vader's turn toward the light side is sudden, Palpatine never fully trusted any of his apprentices and always suspected that he would be betrayed. In Star Wars: Tales of the Jedi, Palpatine tells Count Dooku directly that he doesn't trust him and that he's always questioning his loyalty. He would have felt the same way about his next apprentice, as well. Despite this, Palpatine never stopped Vader before his betrayal.
In Star Wars, the Sith follow the Rule of Two. As Yoda puts it in Star Wars: Episode I - The Phantom Menace, "Always two, there are. No more, no less. A master and an apprentice." By having only two Sith at any time, one Sith teaches the other. Since the Sith use negative emotions, eventually the apprentice will try to overthrow their master. In Star Wars: Tales of the Jedi episode 4, Dooku meets with Palpatine as Sidious, demanding, "You question my loyalty?" Sidious immediately responds, "Always." In the same way that Palpatine/Sidious would always question Dooku's loyalty, he would always question Vader's as well because of this Sith tradition. Palpatine knew Vader had to betray him, so he tried to diminish Vader's power in a few ways.
Why Emperor Palpatine Couldn't Stop Darth Vader's Redemption
Palpatine was able to turn Anakin to the dark side, as he had with Dooku, thanks to his inner turmoil — since Anakin could never fully dedicate himself to the light or the dark side. This inner turmoil would eventually come around because Palpatine wasn't fully able to convert Anakin/Vader into his apprentice, resulting in Vader's return to the light. He tried to take advantage of Vader's obsession with protecting his loved ones when he lied about Padme's death and then used Luke as a final test to prove Vader's dedication to the Sith. By him forcing Luke and Vader to fight one another, Luke was able to keep his emotions in check long enough for Vader to be swayed back to the light and make him turn on the Emperor.
Why Darth Vader Never Turned Against Emperor Palpatine Sooner
In the Marvel Comics series Darth Vader, the titular villain discovers that Palpatine is considering replacing him as his apprentice and decides that he needs to have his own army outside of the Emperor's control. He uses this droid army to take on Palpatine's new apprentice candidate, and the comic ends with Vader and Palpatine each having a newfound respect for one another. But Vader never rebuilds his army, nor does he try to challenge Palpatine in any other meaningful way. This is partly because of Darth Vader's suit, which was intentionally made to cause him pain, both focusing his rage and making it harder for him to fight against Palpatine. In addition, the suit was intentionally made weak to lightning, so that Palpatine could easily strike his apprentice down if needed.
By making sure Vader would be on the back foot in a fight, Palpatine never felt pressured to take down his apprentice. Vader was still terrifyingly powerful against most Jedi and non-Force users, so he was still useful to Palpatine as his enforcer. Palpatine and Vader both knew that their fight was coming, and neither fully trusted the other throughout their entire relationship. Palpatine should've stopped his apprentice in Return of the Jedi, but Vader's win created one of the most iconic defeats in film history.