Heh, same here, I guess the answer is practice practice practice.
I currently cramp up after 25-30 minutes of practicing the fast parts, gradually speeding up with a metronome, so maybe mindless repeating is not the way to go and should try softer attack (but that's not how Mr. Harris sounds like

).
When my right hand is too tired, even after slowing down again, I give it a rest and start "abusing" the left hand with some power chords (I think fear of the dark is an example but I didn't see tab sites mention this, afraid to shoot strangers is another example).
It is hard not to mess up the wrist when playing power chords in low fret positions, so careful with that.