Looking for dramas where the main characters' relationships don't work out (not due to infidelity), they try to fix things, but their feelings waver and they end up separating.  

We Made a Beautiful Bouquet - basically what you look for. it is however a movie, but very good one.
Josee, the Tiger and the Fish - this does also have a korean adaption but honestly the best one is the Japanese one. There is also an anime version however that ends happily. The Japanese one is very raw and has less of s storyline with falling out of love, but they do realise there are things they cannot beat even with love. So the ending is similar to what you wish for.