I'm not saying that it doesn't happen that someone has to take the FE many times but that seems a bit odd given that you believe you've put in a lot of studying time, have the knowledge, feel confident going in etc... You'll have to engineer yourself out of this one. I don't know how hard the FE got since I took it but I remember walking in feeling like crap, walking out feeling crappier but I passed. And that was with completely skipping thermo. I think I picked C for all of them.
First, your random performance seems suspect. I'd want to know if you have a test-taking method. I feel like half of any test is learning to take the test itself. I think the diagnosis might be misleading. Personally, I have a problem with word problems. A problem with one sentence, a bunch of numbers and maybe a graph, I have no issue solving. One that has a bunch of words then I have to figure out 4 word multiple choices is a pain. English is my third language but it doesn't matter what language it's in. I learned this about myself when I failed 3rd grade math.
Second, if you've managed to take it a bunch of times, I suspect you're not giving yourself enough time in between. Our brain has memory that is hard to flush quickly. That's why, if I drive somewhere for the first time and got lost on that first time, the next time I go, I end up taking the same route. As I'm going along, I'm sense I did the wrong thing but keep going until I realize that I actually took the wrong route. It took me 3 years to stop getting lost going to my friend's house though I was going a couple time per month. I didn't stop until I learned a completely different route. That might just be me. But you might want to stop taking the test and give yourself more time in between.
Third, and this is related to the second point, since you're not giving yourself enough time in between, you probably approaching your studying as reviews rather than studying each time. Something is surely not clicking or not enough of it is clicking to result in a passing grade. I find that when I think I know a topic, it helps to focus on practice problems and sample exams. Maybe that will become your weekend for 6 months. I have a co-worker who would sign up for the PE, fail it, then sign up to take it again in 6 months (they're only offered twice per year). He would review for the last 2-4 weeks before the test, take it again, fail it again, then start over. He eventually passed but that's a waste of money, emotional pain and 8 hours of life. I say gather 3-4 practice exams, preferably not from NCEES, and without studying, take the first one. Don't bother trying to figure out things you don't know. Just take the test. Maybe 4 hours on Friday, 4 hours on Saturday, then on Sunday or Saturday afternoon, go over each problem you got wrong or that you couldn't do. Then once you're done, throughout the week, after work, go over each again as they relate to the chapter/knowledge area. Chances are, if you got that problem wrong, just figuring out the solution is not going to help unless the question is always framed the same way. So you need to brush up on the knowledge area altogether until you can answer a bunch of questions from that chapter with few to no mistakes.
Lastly, your test taking skills... If you're finishing the entire exam, not running out of time, picking an answer for each question, then maybe something else is off. When I study, I make notes to myself to get out of the habit of doing certain things. My cheat sheets always have an area for those. And before I take the exam, I know my cheat sheet very well so when I come across one of those bad habit behaviors, it triggers me to confirm with the cheat sheet. For example, I like sequence and I like to keep things in order. But when I take a multiple choice test, I don't waste time on questions I can't figure out quickly so I skip some. But, when I go back to answer, I'm always tempted to bubble the responses in sequence. Imagine if you skipped #4 and #5 but when you get the answer for #6, you bubble #4 because it was the next blank. Now all of your exam is off. I understand with the computer-based FE now, that might be unlikely. Therefore, there might be something else that you're doing that is skewing your answers. There are chapters that I can open my reference book to the exact page I need. There are others I'll look forever before I find. So it's good to tab the reference manual if it's allowed to minimize wasting time. I feel that it's important to learn the material but also learn how to test as well as test with the reference manual. If allowed, I like to have my own cheat sheet glued to or on the inside cover of the manual. I build it up as I go along. So, you have to be able to identify distractors in the responses, forming better habits, increasing speed, use reference effectively etc...
In summary:
- If you've been taking the FE every month, stop. Go enjoy life for 1-2 months then sign up to take it again 3-6 months after that.
- Take a bunch of practice exams and identify your issue areas.
- Study first based on your issue areas by figuring out the solutions, then cover the entire chapter for these weak areas. One problem doesn't expose you to all.
- Take note of your test-taking habits as you go along and write them down. If it's allowed, write them in the relevant chapter of your reference manual and use the manual's interior cover or blank page to write them all down.
- Take note on the type of problems that you do well and those you don't. For me it's calculations. Anything with a bunch of sentences and words are a pain so best left for last. I also think that the diagnosis might not be helping. If you have issues with the word problems versus the calculation problems, you'll never know. It will just look like you're not proficient in Structural Analysis because you only got 40% right. But if 60% of them were word problems that you didn't read right, then practicing Structural Analysis calculations won't change that.
- Since the test has a countdown, consider taking the last 15 minutes, whether you finished or not, to make sure that the answers you intended to chose, are the ones that you did. I took the CA Survey exam recently and it's timed 55 questions in 2.5 hrs. For each question I answered, I wrote down the number and the answer letter I intended to pick. The ones I skipped, I still wrote down the number and put a X next to it. I ran out of time. I gave up on the last 5 questions, picked a letter, knowing there's no way I'd be able to answer them, then went back to the beginning to check my answers. Sure enough, I found 3-5 of them I picked one answer rather than what I intended. They give the options to confuse you. When you're in a rush, N53 25 20E looks the same as N53 25 02E.
Now if you're doing all of this and you're confident that you're doing all of this, then maybe you're ought to just spending money to take it over and over and hope that you pass one day. Just remember the EIT is a preparation as an engineer and the end goal is to get a PE. An EIT might make you more competitive in today's world if you just graduated but it's really not that big of a deal especial if you have experience. The PE is a big deal. If you're having issues with the EIT and you're doing everything stated above and more, the PE will be hell. So, I feel it's worth doing it right and using time in your favor.
Good luck!