I've never posted on here before, although I'm a pro runner and so occasionally ~peruse~ letsrun, but this thread is the SINGLE most informative thing I've seen on the site and so I couldn't resist.
I'm 26 and have had the exact same experience that so many of you have described, starting around the age of 17, and have been met with the same lack of answers/solutions. I've talked to sports med people, endocrinologists, gynos, etc. and no one seems to have a remote clue about what might be going on.
For me it usually happens roughly around ovulation (but sometimes more random), about 3 miles into a run, and goes away after I stop and walk for about 2-5 minutes (walking helps although I usually feel like I want to die). And then I feel fine for the rest of the run, as if nothing happened. The pain is spot on the way other people have described - what I would imagine contractions to feel like, or as if there is an intense pressure twisting in my abdomen. I get it usually on a couple runs a month, but may go several months without feeling it, and I get it after nearly every race. I can say without a doubt that it is the most intense pain I've ever experienced.
I sought out help from doctors etc. when it started to interfere with my workouts (I've had to stop in the middle of tempos before, which is really irritating) and was met with no answers. It is SO, SO relieving to hear that I'm not the only person who has experienced this (although I'm so sorry for what everyone has to go through). I'm generally interested in endocrinology and have thought a lot about whether the pain is related to cyclic hormone fluctuations gone awry, but I have no real basis to go off of other than the timing of the cramps. I have also read that because vasopressin (released when dehydrated) and oxytocin (which causes uterine cramping during birth) are both released from the same place, sometimes your body can accidentally release both when it is only meaning to release vasopressin. Personally, I haven't seen a link between dehydration and the cramping though, so for me that theory doesn't really hold up.
I hope to someday find answers to this and wish I had more solutions to offer, but I will say to anyone who feels like they want to quit because of it - I've somehow gotten to the professional level in running and I honestly credit having to push through this random pain on a regular basis in part for making me tough. I think it's made me develop the skill of talking my body down from a difficult spot and occasionally wonder (when I'm in the 5 min of agony wishing I didn't need to deal with this) if I would have reached the place I'm in without it. So basically what I'm saying is you all are tough as hell, don't give up.