I used to finish books that I absolutely could not stand because I was book blogger & made reviews. when you have a following of people, I think it's best to write your honest opinion about what you like & dislike (which is helpful for anyone who has a similar taste), so I imagine those who are serious about their drama blogs & drama reviews finish dramas they hate for similar reasons.
as someone who's not into reviewing her dramas, tho... I have finished a small amount of dramas I didn't like. if I think it's pretty bad I will let it go anywhere between episodes two through six, or sometimes I leave halfway through episode one, but the dramas I started out enjoying are a different story.
I either stick with them out of a weird sense that I just gotta finish it or I'm already close to finishing it. other times it might be because I'm loving the skill of an actor or two, or maybe it's a character I'm digging. like the writer of sassy go go upset me more & more as the show went on, but I basically stuck it out because I thought chae soo bin was brilliant + there was ji soo, & his & lee won geun's characters were also worth watching for.