leg cramps in high intensity intervals

I am getting quad cramps toward the end of interval workouts. I don't seem to get them as much in distance work. One of my favorite workouts is 25 x 66 yds on 2 minutes. The first ten are usually 50 sec and then I slow to 55. I start cramping on the 20th rep. It happens on push off when the quads want to lock up and also the calfs a bit less. It ends up ending my workout. I notice that if I extend the rest interval longer (because I am talking to someone....or just plain stalling), it brings on the cramping earlier and worse. Is a minute rest a no no? Should I lessen the intensity and reduce rest for this workout? Yes I eat bannanas and drink plenty. Why the legs and not the upper body muscles?? When I used to run intervals sometimes I would get chest cramping of all the places, but never the legs!! how ironic.