I'd heard it's the fact your diaphragm moves up and down on the elastic ligaments inside you as you run (as do all internal organs) and can get out of synch when you run and then pulls down when it should be moving up, hence the pain as it cramps.
Or it's also possibly because blood flow is reduced to it as you run, again causing cramps. They 'aren't sure' apparently.
Damned Diaphragm. Tis that pesky thing that hiccups come from! It's like a joke internal organ!