I get what Every ne is saying. Anither problem I've recently run in to is Boys over flowers isn't terrible and I like the f4...but God I'm so hired 7 episodes in. I want to finish it but it's just boring where I'm at.
Mostly from the first episode
If it cast my fav actors, i'll give it a try until episode 3
Dang, from what I can see you are struggling with the exact same K-dramas I struggled with LOL

Birth of a Beauty was my first 'official' K-drama so I liked how dramatic it was, but the second half had so many waste/filler episodes I almost didn't make it to the end. The ending is expected I just wish it came around faster.

I'm not sure which Boys Over Flowers you are watching, but from my experience the Japanese one was sooOOOooOOOOO CORNY as soon as I finished it I marked it as completed and never looked back. I forced my way through since it's such a huge classic but it does not deserve that hype lol
I tend to stick to the 4 ep rule. If the drama isn't good or moving along by the fourth ep, I'll definitely drop it. Occasionally, there are a few dramas that I try to stick with because of the cast (I know, a dumb reason haha). In these cases, I try to watch until the eighth ep before deciding whether to officially drop or not. :-)
I saw someone mention descendents of the sun...and I started it, put it on hold.  Was housesitting, cleaning up to leave and decided to pick it back up...since it was on netflix....and got sooo hooked as I was getting ready to leave and was gonna be busy for a WHILE.....I was very sad.  

depends on how annoying the characters/actors are or the drama itself is just meh, can't get into it. I give it a few episodes. I dropped Criminal Minds, it wasn't that bad but I just couldn't stand all the violence anymore (I know given the genre it would be like that but still)

Usually 1-3. If I can't get in to the plot or see something I don't like. I'll just stop.