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He will, don't worry.
It's true that Jin-Woo's father does die in the upcoming chapters. Actually, the reason he dies is due to protecting Jin-Woo when he's temporarily unconscious during an unbalanced fight against several monarchs at once. In order to be able to do that, he has to fully use the powers of a Ruler, despite knowing that his mere human body would be unable to withstand them and would eventually disintegrate as a result of using them.
However, in the end of the story, Jin-Woo decides to reverse time to deal with all the Monarchs sooner, before they can do any damage.
So everyone will be alright again eventually, and Jin-Woo gets to live happily with his entire family again :)
spoiler
something gonna happens in korea lol lol pls ready your tears qkhsmwjajajajjajaja