Since everything is connected to the top square, that's really the only part of the printer that needs any "stiffness". The top square uses a double o-ring grip on each vertex, which is pretty solid. I've moved my printer all over my apartment and taken it in my car to various places. It's been fine. Once the orings are well tightened, you'd have to really yank on it to get it to slip.
I typically print around 100mm/s and it handles that easily. I've printed at 3 times that speed with really high accelerations, and it's still fine (not that I would recommend doing that). On a machine like this, you'll spend probably zero time worrying about the frame, and more time worrying about the gantry torsion inherent in h-bots. I've mostly gotten rid of that with a few modifications which are discussed on the hbot google group.