Despite numerous chances to bring him back to life, King Kai has remained dead in the teaching Goku the Spirit Bomb and the Kaio-ken technique was killed during the Cell Saga. When Cell threatened to destroy the Earth by self-destructing, Goku used Instant Transmission to bring him to King Kai’s planet, thus sacrificing himself, King Kai, Bubbles, and Gregory to save Earth.
King Kai was a ing character in nearly every saga of both Dragon Ball Super. After training Goku to beat Nappa and Vegeta, he spectated from his homeworld and watched the Z-Warriors’ battles with foes like Frieza, Cell, Majin Buu, and Beerus. He was also one of the characters allowed to observe the tournament between Universe 7 and Universe 6. Much to his annoyance, the fact that his planet exists in the Otherworld hasn’t stopped Goku from periodically visiting him for training purposes. Being dead hasn’t affected his presence on the show, as he, Bubbles, and Gregory all able to continue staying on his planet and interacting with Goku and the others.
In the Dragon Ball franchise, most of the main characters have died at least once, and have had to be brought back with a wish from the Dragon Balls. One character who hasn’t been resurrected is King Kai, who has been dead for over ten years now. There was a seven-year time skip between the Cell Saga and the Buu Saga, so a resurrection wish easily could have been made during this time. As for why it wasn’t, it would seem that saving him unfortunately just wasn’t a priority for the Z-Warriors. Though Yamcha, Tien, Chiaotzu, Piccolo, and Krillin have all encountered him in the past, they didn’t have a strong connection to him. Sadly, since he lived on his own planet anyway, his presence was never really missed. The only Z-Warrior friends with King Kai was Goku (who was also dead at the time).
When Goku returned, he too didn’t make a move to resurrect his mentor, even though four years ed before the beginning of Dragon Ball Super. A conversation between the two characters finally shed some light on why no one has thought about restoring King Kai to life. After blaming Goku for his death and pointing out that he’s still dead after all this time, Goku defended himself by saying that he forgot, and that for King Kai, it doesn't matter if he's dead or alive, since there doesn't seem to be a difference. This of course infuriated King Kai, who argued that death actually does limit him physically.
A later episode of Dragon Ball Super indicated that Goku’s friends share his opinion about King Kai’s situation, and that they too either don’t care about him, or have simply forgotten about him. After over ten years since King Kai died in the Cell Saga, Goku finally gathered the Dragon Balls with the intention of wishing back his mentor. However, the other main characters argued with him over what the wish should be, wanting to instead to ask for much more trivial things. When Shenron grew tired of waiting for them to come to a decision, the wish was wasted and King Kai, Bubbles, and Gregory were forced to wait once again for another opportunity. Looking at how much effort has been put into resurrecting King Kai so far, it’s likely that the character will still be dead when the next Dragon Ball anime kicks off.