While there are things that I enjoy in K-dramas, things that will move them into the "potential favourite" category, I have noticed over the years that I'm lying to myself.
I've said things like "Oh, this contains trope XYZ, I will love this" and I still ended up dropping the drama, leaving it rotting on my "You disappointed me" pile.
So, I've asked myself "What makes me love a drama, truly? Is it something specific?" and I've come to realize that, yes, it is something very specific. All my favourite dramas don't suck in their second half or towards the end.
You probably know what I mean, right? You watch an absolute fantastic drama, mindblowingly awesome, and then, around episode 10-12, the plot becomes weird, lackluster, you're not all that keen on clicking on the next episode. "Oh, so she's hiding the truth by telling him that she doesn't truly love him, to drive him away, to be noble...again. Like, how original, I've never seen that onebefore... *sigh*" 
So, my question, to you, without naming any dramas on my own, just to be neutral: 
What would you say are K-Dramas that don't suck during their second half? 
Meaning, the plot doesn't drag, there aren't any unnecessary misunderstandings to make the drama longer or any weird dramatic plot twists, the plot doesn't contradict itself etc.
Please recommend them to me, but please, do it responsibly, I will probably end up watching them. Don't lie, don't sugarcoat. If it sucks towards the end, better not recommend it to me, I'll only give it a bad rating later on.
Thanks in advance guys!

EDIT: Thanks already for the recommendations, I will make a list here so that new people can see what's already been mentioned.

49Days
Age of Youth
A Gentleman's Dignity
Bad Guys
Beautiful Mind
Cruel City
Faith
Good Doctor
Last Night Restaurant
Liar Game
Love Me If You Dare
Mask
Misaeng
Missing Noir M
Plus Nine Boys
The Moon That Embraces the Sun
The Vigilante in Masks
When A Snail Fell in Love
White Christmas

Dramas you recommended that I've already watched:
Another Oh Hae Young (will always be in my top list, very nicely paced, female lead knew what she wanted, that alone gets a thumbs up from me)
Healer (one of my favourites, didn't let me down)
Kill Me Heal Me (very enjoyable, female lead needs to work a bit on her acting, other than that, great drama)
Oh My Venus (Liked this one a lot, many said it was boring that they got together so soon, but to me I prefer this cute domesticity to over the top and unnecessary drama.)
Pasta (Also all-time favourite, both protagonist always spoke their mind, had backbone and no secrets, which was refreshing)
Pinnochio (Sadly, first half was great, could have been over after episode 12 or something though)
Queen InHyun's Man (Very cute, can recommend, didn't get boring)
Splash Splash Love (Very cute and short, with only two Episodes it couldn't really turn bad in the second half, though, right ;D )
W - Two Worlds (Sadly, same fate. Was awesome until the dreaded and over-used amnesia plot)

Dramas I can recommend (in addition to the above ones):
Coffee Prince - Old but gold, is all I can say.
Sungkyunkwan Scandal - Refreshing rendition of the typical gender-bend trope, may remind some people of Moonlight Drawn over Clouds but I prefer this one.
It's Okay, That's Love - Can be heavy for people who are used to typical romcoms, as this deals with psychological problems, but I love Gong Hyo Jin so yeah

Can't name many more, sadly, I have lots of dramas I also enjoyed but I would be lying if I said they didn't drag towards the end. It's seems to be a thing with k-dramas.
I can recommend two Because I loved them!! 

Mask - Korean drama... This one catches our attention because the characters are superb!! I loved everything in that Drama even the Villain, The cast, the plot, the drama, developing of characters and feelings... Oooh this drama is amazing..

And another that isn't Korean but Chinese, the vigilants in masks...
I loved this one because it's full of emotion, adrenaline, fight, love, drama... 

I hope you enjoy them like I did... I'll re-watch them
I see that you've seen healer & pasta so I'll suggest what I didn't see on your completed list:

misaeng/incomplete life - my gold standard, 10/10. I was highly impressed. fair warning that it starts out bleak but it is one very touching & inspiring story that warms the heart.

liar game (korea) - I was not very into this & seriously questioned the writer & even the pd through about the first four episodes. after that I either stopped caring, stopped behaving like nitpick, or the writing/directing legit improved (...& the painfully forced one-side romantic interest from the female mc to the male mc is dropped somewhere between eps 3 - 5?), but I have a nice memory of this as solid, suspenseful fun. altho there will be problems if you're a big fan of the jdrama &/or manga & can't look at the korean adaptation as a separate entity.  

49 days - it's been some time since I have seen it, but I don't remember it being illogical, contradictory, or at all a letdown. (minor?) spoilers: *I think there is a misunderstanding between a side couple that took place in the past, but they are able to bittersweetly reconcile.* I did feel a little tricked at the end where just as I thought everything was good, it wasn't. I cried & got over it, & it's remained a favorite drama of mine. 

age of youth - a refreshing, well-done drama about the lives & relationships between five different ladies who live together, & it's only 12 episodes! I will say that I've noticed younger people, especially those in their twenties, seem to respond the best (considering that the drama depicts women who are also in their twenties...). in particular I've seen that older women don't click well with this one. as a head's up: ye eun is slightly annoying/frustrating at times, but I loved watching her character develop & change. 

cruel city - maybe the only reasons for me not to suggest this is if you dislike violence, slower pace, & sad endings. it's intense & a little darker than most kdramas, which is partly why I like this tbh, & altho it doesn't end happily I also don't feel that it's an inappropriate or illogical end that should make you rage at the writer. 

missing noir m - a surprisingly good procedural to come out of korea, IMO. it does have a HUGE cliffhanger end that leaves me hoping for a season 2, tho.

white christmas (2011, 8-ep special) - l was so hooked that I finished this in a day & I loved every second---I love it so much, in fact, that I pay little notice to the illogical shortcomings seen in the last episode. if you're not into this by the end of ep 1, then it is likely not your cup of tea. plus, if you're not head over heels then the flaws in the writer's logic in ep 8 may ruin it for you. side note: same writer as the age of youth.

late night restaurant - really simple & easy-going slice of life kdrama based on shinya shokudo.

plus nine boys - introspective romcom that I really enjoyed about three brothers & their uncle. there is a love triangle that actually becomes a love square, if I remember right, but it's one of the rare instances in which a loveshape that didn't bother me. it might feel a little painful, tho, since they are all friends & the second leading love interests of the primary pair are genuine about their feelings.
I know what you mean.  A lot of them kinda run out of plot and then try to drum some up.  That's what I've noticed the trouble is, they try to keep going with something that didn't have enough plot.  That's why a lot of the action and the fantasy ones don't seem to have this trouble, and can have more episodes, there's more content for a writer to work with.  Not sure I have any suggestions because to be honest I haven't watched all that many, and there have been a few I've dropped.  Or they disappeared when I was halfway through them on Netflix.  I did love Faith, and never felt like it ran out of plot.  Otherwise the ones I've liked were based off fairly long and successful manga...and the manga were already good, which is why they were made into dramas.   
Not sure of your tastes but I'll list the ones I couldn't put down:

W
Another Oh Hae Young
Kill Me Heal Me
A Gentleman's Dignity
Pinnochio (the last four eps of this are phenomenal)
+1 Cruel City, Mask
Bad Guys
Beautiful Mind
Good Doctor
I am just like you so you are not alone hahah for me it has to be exciting, unique and that it doesn't drag with unnecessary things to go on my favorite drama list. You didn't say which genre but I have become a fan of action and mystery since Love me if you dare, the cases where amazing and it also had romance in it. So in Action Mystery 
Love me if you dare
When a snail fell in love (don't expect romance)
 
Other genre
Another Miss Oh (This is my ultimate favorite Asian Drama, I felt like I was going to have a heart attack because my heart would beat so fast with excitement)
Cruel City (Very good drama)
Splash Splash Love (Amazing Historical drama)
Age of Youth (Unique fun drama with a hint of mystery)
Queen In Hyun's Man (Amazing leads chemistry)
Oh My Venus (Perfect Mix of everything Romance, comedy, etc etc)
The Moon that Embraces the Sun (One of the best historical dramas I have watched)

I am probably forgetting some great dramas but those are amazing. But remember I may think they are the best but is not for you. =)
I am just like you so you are not alone hahah for me it has to be exciting, unique and that it doesn't drag with unnecessary things to go on my favorite drama list. You didn't say which genre but I have become a fan of action and mystery since Love me if you dare, the cases where amazing and it also had romance in it. So in Action Mystery 
Love me if you dare
When a snail fell in love (don't expect romance)
 
Other genre
Another Miss Oh (This is my ultimate favorite Asian Drama, I felt like I was going to have a heart attack because my heart would beat so fast with excitement)
Cruel City (Very good drama)
Splash Splash Love (Amazing Historical drama)
Age of Youth (Unique fun drama with a hint of mystery)
Queen In Hyun's Man (Amazing leads chemistry)
Oh My Venus (Perfect Mix of everything Romance, comedy, etc etc)
The Moon that Embraces the Sun (One of the best historical dramas I have watched)

I am probably forgetting some great dramas but those are amazing. But remember I may think they are the best but is not for you. =)
Rooftop Prince
I Hear your Voice
Descendants of the Sun
Something about 1%
You're all surrounded
Legend of the Blue Sea
Goblin
Yeah there are many kdramas that a little bit draggy in second half and sometimes I ended up dropping it or just fast forward so this are the list that I really look forward until the end.

Cruel City
Beautiful Mind
Fated to Love You korean version
Oh My Venus
Winter Sonata
Sassy Girl chun Hyang
Stairway to heaven
Princess Man
Deep Rooted Tree
Cheese in the trap
Age of Youth
Full House 2004
Cruel City
Age of Youth
Misaeng