I recently did a bunch of bokken work and after just a couple of days, my lower back was killing me. And for the first time I seriously thought, maybe the highly respected teacher who taught me this way made a mistake. Or maybe he just never bothered to correct the mistake I made over thousands of cuts in his presence. Maybe he doesn't really cut that way, himself. Maybe he has lower back trouble, too, and just bears it, which could explain a bit about his personality. So I've been doing some serious re-evaluation of my most fundamental use of bokken and I see some things in the clip that could be interesting to work with.
I'll bet you arch your lower back while doing sword work. That both makes your lower back sore and makes you unstable, tending to tip backwards. Studying a video of yourself might be more useful than studying this (or any other) video.