Ronsr, the issue would be shutting the screen off or “turning the page” when the Shem Hashem is on it, not deleting the file.
I’d never heard of this before, but in a post wiped out by the Post’s attack on YWN, someone mentioned that these e-readers work differently than regular screens.
Midwesterner had said that he asked a shailah (about computer screens, I guess) and was told it’s muttar. Computer screens are constantly refreshing themselves, so one never really erases anything, he just prevents it from returning, which isn’t a problem.
E-readers, OTOH, have the image of the letters “etched” into the screen, and turning it off might be considered m’chikah.
The tzad to be meikil, of course, is that Syag bought one for her son.