Dramas that definitely fit your criteria.
Love Rain - You’ll have to make it through the first 5 episodes about the parents’ generation in the 1970s before you get to the main couple, which fits your criteria.
The King's Woman
With these three I don’t remember well enough to say if ML was rejected, but he definitely falls first, and FL is hesitant to start a relationship with a younger man.
I Hear Your Voice
Sapuri
Hajimete Koi wo Shita Hi ni Yomu Hanashi
Some dramas that almost fit your criteria.
My Secret Romance - It starts with them having a one night stand. She leaves before he wakes up. He remains hung up on her, while she tries to pretend it never happened. I think that’s kinda like getting rejected.
Second Love - This fits your criteria. ML falls first, FL rejects him. However, their relationship starts very fast, so she doesn’t reject him for more than 1 or 2 episodes.
Last Cinderella - He does get rejected repeatedly in the beginning, but he hadn’t fallen for her at that point (his step-sister had paid him to date her).
Descendants of the Sun - She initially agrees to go out with him, but breaks up with him soon after they start dating, then is resistant to restarting their relationship.
