the male lead breaks the female lead heart at first (or does something else....) and after that he tries his best to convince her of his love , asks for forgiveness something like" new tales of gisaeng " thanks for your help ^^
I think Smile Again does this (I haven't finished it - but he does break her heart)
Emergency couple is something like that.
Fated to Love You - The original's taiwanese, but there will be a kdrama remake in July :)
What is love Miss Korea - happens before the show starts Say that you love me And i second Smile again
Que Sera, Sera - is just like that, one of the best, trust me
I could not think of anything exactly like you are saying but.. sang doo, lets go to school - Guy does lots of things to try to get the girl back.. even goes back to school as a high school student while she is a teacher. He did not really break the girl's heart but they did separate for a pretty long time.. proposal daisakusen - He does not break the girl's heart.. but never lets her know how he feels. He goes back in time to try to fix things he did wrong in the past to try to stop her from marrying some other guy.
Have you seen Master's Sun? or Smile, You(it has 45 episodes though) or C-drama Say That You Love Me(chinese version of It Started With a Kiss) But I think Say That You Love Me fits the storyline you want. :)