For starters, things could be much worse: I would argue that SC is more quickly "improvable" than CR and RC for most people. If you're a crappy, imprecise reader, you probably won't become great at CR and RC just by reading a test-prep book. If you're scoring in the 36-39 range on verbal while struggling with SC, that's actually a good sign, in my book. It sounds like you have some solid underlying verbal skills... and the SC section is absolutely conquerable if you put in enough time and effort.
The tougher part is figuring out exactly why you're struggling with SC. Are you from the U.S.? If so, it's entirely possible that you've never really learned grammar in a structured way, so it can be tough to learn to approach SC questions in a mechanical, systematic, methodical way. (Full disclosure: I'm from the Midwest, and never learned a lick of grammar until I was in my twenties. Sad, but true.) I might be way off here, but I'm wagering that you have a hard time "turning your ear off," and you probably go mostly by sound--and that will cause a lot of bad SC errors.
I'm not sure what, exactly, will get you headed in the right direction, though. A lot of people really like the PowerScore and Aristotle SC books, but the MGMAT book
covers much of the same ground, so you might already have maxed out your ability to pick up SC methodologies from books. Maybe try poking through a copy of the Aristotle grail, and see what you think? My fear is that it's mostly an approach problem, though--you might already know the rules, but struggle to recognize them in the actual questions. That's improvable, but it might take a lot of practice, and maybe a little bit of guidance from a course or a tutor.
Am I on the right track at all? I'm assuming that you're a native speaker (maybe from the mid-Atlantic somewhere?), but I might be way off...
Helping students kick the GRE and GMAT in the nuts since 2002. http://www.gmatninja.com.