I usually push on! Leaving dramas incomplete drives me slightly insane... But then there are the dramas I can't watch another episode with. I don't like to drop them though, so I put them on my On-Hold list and then watch like one episode every few months, lol.
i'm not the type to force myself... if i don't enjoy it within the first episode or two i will stop watching. i have limited time these days so if i'm really not enjoying it i probably won't make it past 30min of ep1 *_*
Even though I have a ton of time on my hands, I can't be bothered to waste any of it on a drama I'm not enjoying. Thankfully I'm easy to please so I haven't dropped many. If I'm not really feeling the first episode of a drama I'll try the second on, if I still don't like it than I drop it/put it on hold. Sometimes, it isn't that I don't like the drama but rather I don't care so much as to find out what happens next.