He can't give up because that means she'll die after marrying the ML.
I have theories about where this story is going bc it seems pretty obvious to me: MC and ML were the OG! couple, but MC was the one who kept on dying so ML decided to go after Daphne to spare him. And MC spent 47 lives trying to save Daphne, so he thought he loved her. But in the 48th life he decided to pursue ML, and he'll realize he doesn't really love Daphne.

I need a proper justification for the MC's feelings towards Daphne, because to still love someone who rejected you over the course of 48 lifetimes isn't normal. At this point it's obsession and I would love to know why he's obsessed