My hand gets tired in this work too. It's always a challenge for me in perpetual motion movements.
I do two things to combat it: (i) find any millisecond I can in which to relax the left hand, and relax it completely. Tension builds and becomes cumulative. It's important to reset when you get the opportunity. (ii) Practice with a very light left hand, such that you let a lot of notes buzz from lack of pressure. What you'll realize is that many of the notes DON'T buzz, even though you're barely pressing. It will highlight for you that you're pressing harder than you need to much of the time (as we all are) and will acquaint you with how little pressure you really do need.
I have to consciously remember to do both of these things, and do them often, to keep my hand light and loose all the way through.
Amateurs practice until we get it right; professionals practice until they no longer get it wrong.
1999 Dake Traphagen (spruce);
2008 Dake Traphagen (spruce, double top);
2010 David Pace (cedar, double top);