If it's the rest of that beam, then just glue the sucker in. The circular pieces above and below it would support it fine. If you can't find the rest of the piece you may want to reprint it though.
The picture supplied is fairly low resolution, so I can't be totally sure though.
I know pepakura can be one of the more stressful steps in the process, but you have to find the method that works best for you. Scissors are not as exact as an exacto knife, but they're a ton safer, and not that much worse at cutting the paper, if you get used to precision scissor cutting. So if the knife is not working, you may want to try something else. I know that as an exacto blade gets duller (which happens FAST when cutting cardstock) it starts to drag, and catch the paper, weakening or tearing the paper in the process. I have moved away from exactos, and now use either box cutters for precision work, or scissors if I want it done faster and safer.
I don't think you should abandon the work. Keep at it and it will soon become reflexive as you get more comfortable with cutting cardstock. You have a lot of talent and I'd hate to see your efforts so far tossed! Good luck, and the site is here to help you!