I had the same problem as you. My first verbal score with absolutely no prep was a 46. When I sat the exam after over a year of preparation, I walked out with a V41. Scores in between varied from 40-45, which for me meant the difference between a 710 and a 750.
I eventually identified the problems though, and here's my advice:
1) For RC, you might have to just go with your gut. I found it's very hard to improve here, but practice will help. The only strategy I can recommend is to get in the habit of predicting the answer before you read the answer choices. If your prediction matches an answer choice, you can be 95% sure you got the question right.
2) Develop a strategy for CR. For CR, I found the LSAT "Logical Reasoning Bible" the most helpful tool there is. The LSAT LR questions are almost identical to the GMAT CR questions, and the LR Bible breaks questions down into questions types with strategies for each. For example, in strengthen questions, you have to identify the unstated premise (assumption) on which conclusion is based. Of the 5 answer choices, most will ignore that assumption, usually one will weaken the assumption, and one will strengthen it.
3) For SC, if you're a native speaker, use your gut, but also read the OG SC prep closely. There are certain grammatical errors your ear might have grown accustomed to (e.g. agreement errors, logical predication errors, etc.) These two show up all the time, and it might not be obvious. For example, "Microsoft bought out their competitor when they realized their success posed a serious threat" sounds correct to most Americans, and we all understand what it means. But it should read "Microsoft bought out
its competitor when
Microsoft realized
its competitor posed a serious threat." See the difference?
4) Look for grammatical errors in the answer choices first, then choose based on style. The test makers sometimes design SC questions to trick people who rely on instinct. They do this by including minor grammatical errors in answer choices that are more concise and natural sounding than the correct answer. For example, you might chose "Her business was interested in profits and keeping customers happy." where the correct answer is "Her company was interested in profits as well as the happiness of customers." The second one is wordier and feels like bad writing, but it doesn't make the same parallel structure mistake with "profits" and "keeping."
5) If you usually finish with time to spare, use it instead at the beginning of the section. Getting one of the first ten questions wrong hurts your score much more than getting one of the last ten questions wrong. This isn't true for quant, but it is for verbal. In quant, you can get 10 questions wrong and still do well. In verbal, the first ten question are weighed VERY heavily, and the difference between a 37 and a 47 might be only a few wrong answers. This explains why getting more questions wrong at the end hurts you less than fewer questions wrong at the beginning. It's just how the GMAT algorithm works.
6) Don't rely on test prep companies' sample verbal questions. They usually aren't well written and the answer choices are hard to predict. Their correct answer might have style problems you won't find on the actual GMAT. GMAT test makers are expert writers, so the correct answer choices always make sense to someone familiar with English prose. Not true of the test prep resources. In the past two weeks, I've done the first 60 OG CR and first 60 OG SC questions. I got two CR questions wrong and only one SC question wrong using the strategies I mentioned above. On the other hand, when I did the first 10 SC and and CR questions of an online test prep course I bought, I got about half of them wrong. The answers never made sense. I quit because the questions were making me question the strategies that helped me do so well in the OG.
7) Finally, make sure to take your break after quant. You might think you bombed the quant section at this point in the test, but it's imperative you realize that you simply cannot determine how you did until the end of the exam. If you mull on this, you'll be distracted for the verbal section and get the most important questions wrong because of anxiety. That's what happened to me. My final quant question was the easiest one of the whole test. I assumed that meant I must have done horribly. Because I wanted my score as fast as possible, I skipped the break. At the start of verbal, I kept thinking, "What if I have to cancel my score?" "Will schools reject me if I do?" "Can I really submit a score report with a 650 without killing my chances?" I must have gotten so many easy verbal questions wrong. In the end, it turned out my quant score was actually very high and my verbal dropped considerably because of anxiety. Don't let this happen!
Hope this helps!