Near the end of the Cell Saga, Cell inflates its body in preparation to destroy the earth, but Goku thwarted its plans by teleporting it to King Kai's planet. As a result, King Kai and Goku were both killed by Cell's explosion. After Cell was finally defeated, however, they used the Dragon Balls to revive everyone killed by Cell. Goku wouldn't be revived since he was already brought back once, but shouldn't King Kai, Gregory, and Bubbles have been revived? Cell was the direct cause of their deaths.
When Goku was talking to them he explained that King Kai could have been brought back to life by the wish but refused so he could stay with Goku and guide him around, but why he needed to be dead for this was never explained. Two fan theories I've read to explain this is that he couldn't enter heaven unless dead and that by being dead he could ignore his duties as North Kai, neither of these make sense to me though as we see a lively South Kai in heaven in the manga and we cannot say what is actually required of him in regards to his Kai duties of which we assumingly see him having resumed back on his planet in Super whilst still dead.
So to get back to your question he chose not to be revived at the time and Goku never attempted to revive him since, due to forgetting and not seeing it as a big deal since he's a god, until King Kai expressed his desire for it.