I had the same problem for the better part of four years, seeing various MDs (primary care, Neurologists, Orthopedic doctors, and Surgeons), physical therapists, and chiropractors. The MD’s had said my left SI Joint was hypermobile. I have had only one chiropractor along the way who would give me an adjustment that would provide instantaneous relief, however it would not last more than a day or two.
Finally, a year ago, I found a physical therapist, who gave me the most thorough evaluation I have ever had. He said that the joint was actually Hypomobile, and was stuck in a misaligned state due to the jagged nature of the iliac and sacral surfaces, which comprise the joint. He then used Muscle Energy techniques to realign my SI joints, my T and L spines (apparently having on SI joint out of whack for years messes a bunch of other stuff up upstream), and correct a leg length discrepancy. The technique uses your own muscle contractions with the legs positioned in various ways, sometimes against light resistance from the therapist, to realign and restore mobility to joints. Right after my first visit, my SI joints maintained their alignment and left me pain-free and feeling like I had felt immediately before I had done that last deadlift rep, which injured me 4 years ago. Now I still had some mobility issues that weren’t addressed, but I used Starrett’s videos and his book to help correct them, and I feel I have made major strides in that area as well.
I’m assuming the therapists that you have seen were like those I saw (before the last one that fixed me up) and only gave you a bunch of stretching and/or strengthening exercises, without paying much attention to alignment or gait issues. I’d encourage you to find one who utilizes Manual Osteopathic Techniques and Muscle Energy to correct low back/pelvic girdle dysfunctions.