I've had that issue as well! The screen protector lays perfectly on the screen, but for some reason, the cases with a front bumper always seem to lift the protector on one of the sides. It's almost as if the glass sits a little higher on this phone? I never had this issue with the M7.
Same problem here. Sup Case II and Verizon branded glass screen protector. My mate's Note 3 can't seem to keep them on too and uses a different case that also has the slight front lip.