Hi! I'm glad that Elaine is helping you—she's great!
First, I just want to mention that 40-41 and 710 are already great scores. I know you want more—I'm just saying that you've come really far already. Remind yourself to be proud of that when you're getting too frustrated.
Okay, next, to go from V40-41 to V45 is the equivalent of going from Q47 to Q51. V45 is the 99th percentile. Even though the scale technically goes up to 51 on V as well, only 1% of all students score V45 or higher (and very, very few score above V47).
Why am I telling you that? Because it means that you have to be almost perfect on V to hit the 45 level. As always, "perfect" on the GMAT does *not* mean getting everything right. You'll still probably answer 7-8 questions incorrectly. They'll just be even harder questions.
The first step is low-hanging fruit: How often are you making careless mistakes? You can't afford to miss things that you really do know how to do, not at the V45 level. You'll need to tighten up your processes and be super systematic / anal if you find that you're making more than about 1 careless mistake per V section.
When you're not making careless mistakes, the hardest verbal usually comes down to one thing: being able to distinguish between the correct answer and one really tempting wrong answr (occasionally two—but usually just one at this level). Basically, when you miss something on verbal at this level, it's because you
(1) thought that the wrong answer was better than the correct answer, and probably also
(2) doubted / disliked the correct answer.
So your task, when you do get something wrong, is to really understand how they got you to make those two mistakes on that question.
When #2 occurs, I would start there. Why did you dislike the correct answer? See whether you can explain it out loud (if you can, then you've really understood why). Now, your task is to learn that this thing (whatever it was) is fine. Don't cross off answers for this reason.
For example, someone will say (on an SC), "It sounded wrong." Which part? At what point did the sentence start to sound off? Now, this is the right answer, so you are allowed to construct a sentence using this structure that sounded funny to you. Write a couple of sentences yourself that use that same structure. Put them on flash cards. Drill your brain to learn that this structure is fine and, next time, you don't want to cross something off for this reason.
#1 will always occur. Here, you'll need to figure out the disconnect between what you thought was okay (or better than the correct answer) and why the answer was actually wrong. It might be that you were focused on the wrong part of the answer—the part that you thought was okay was in fact okay, but there was another part over here that made the answer incorrect. Alternatively, it might be the case that you were wrong about the part that you thought was good—it might have actually been wrong for some reason, in which case you'll need to figure out why. Sometimes that reason is also tied to why you thought the right answer was incorrect.
When you do figure out why, try to distill that into a broader lesson to learn. For instance, years ago when I was studying CR, I noted that I was sometimes crossing off correct answers because the language in the answer choice wasn't an exact match for the argument. The correct answer did use appropriate synonyms, but I was getting distracted because there was another (really tempting) wrong answer that did use exact language matches from the argument. So I ended up doubting the correct answer and instead choosing the incorrect answer with the language match because that seemed better.
Upon review, I realized that the incorrect answer would indeed match the language from the argument, but it would "jumble up" that language in some way that changed the meaning—so it was actually incorrect. But I wasn't noticing that part because I was focused on the fact that the other answer's language didn't match exactly...and so then, in comparison, I liked this wrong answer because the language (superficially) matched.
I finally realized that I could cross off answers if the language didn't match AND the words used were not appropriate synonyms (eg, the argument said "most" but the answer choice said "all"). But I also realized that I should NOT cross off non-matches that were still appropriate synonyms (eg, the argument said "most" and the answer choice said "many"—that's acceptably within scope). And I realized that, when I did see exact language matches in an answer, I needed to read the whole answer holistically to make sure that the meaning conveyed was actually the right meaning—if not, I'd cross that one out despite the fact that the language match looked so good.
So that's the level of analysis that you're trying to get to in order to hit a lofty 45 on V. It's not easy—but it can be done with dedicated work and a super-consistent process! And since you are working with Elaine, this would be a great thing to dig into with her. Bring her a problem that you've struggled with and see whether you can really explain what your errors were and how not to fall into those same traps next tiem. Or, where you know you can't figure it out, bring that to her and discuss it so that you can figure it out together.
Try that out and let me know how it goes.