My problem with Korean dramas

I can totally relate with you. I like the start when everything is so exciting; but when the main leads start to fall in love and then become too mushy-I just become too tired. That's why more than half of my dramas are dropped.

AGREE. i have the "7th episode curse" where i can't get passed episode 7 because it becomes dull, thats why I have watched about 150 dramas but only finished like 20 ;A; but when i do finish a drama i put it on the highest pedestal (i recommend 49 days, if u havent watched it , never a dull moment)

I recommend watching J-dramas too, however, as I have the same problem as you do but i never experience the dragging when watching j-dramas (somehow they know how to tell a story better in an engaging way even though in k-dramas there is better acting and cinematography) i recommend: 
http://mydramalist.com/45-yankee-kun-to-megane-cha...
http://mydramalist.com/10-taisetsu-na-koto-wa-sube..
http://mydramalist.com/12190-gakkou-no-kaidan-2015
http://mydramalist.com/32-nodame-cantabile
^ all of which are never dull (all of them are cute romance but if you looking for drama at every corner, on the edge of your seat, I would start with Taisetsu na Koto wa Subete Kimi ga Oshiete Kureta)

i disagree also though, i feel like it would be more engaging if there were less episodes like 13 or 8, so the dragging out the story wouldn't occur (Hotel King was such a victim of that, such a good story!! but too many episodes...).

I agree with you since it happens to me with a lot of dramas, but for Healer, I actually finished it. I got stuck around the same episode as you, but since I liked the beginning a lot, even more so then most dramas ive watched, i pushed myself to finish it. What ive learned is once you've reached that point then you give the drama a break and try something else. Once you've stayed away from it for a while then you go back to it and it wont be so overbearing anymore, but of course that doesn't happen all the time and sometimes you just need to drop the drama. Another person mentioned watching j-dramas which ive done because lets face it they tend to be much better although i would like it if they were just a bit longer.

OMG yessssssssss! I always tell people that I have problems when I reach the ep 10-12. I felt alone in this but as I see it apparently many people think the same. I notice people are recommending you Secret Garden but up until this point I haven't been able to complete it because when it reaches the ep 12 something happens and it becomes pretty boring. I even rewatched it but I can't get pass through that episode.