Weird. I just restarted my game, and the fast mode button is still there. It showed up after my first death, so I know you don’t have to complete the game successfully.
You can access the settings menu, right? It’s just that one button that’s missing?
Yep. The last button on my settings menu is Start Over.
It also doesn’t seem to remember that I don’t want sounds and music, I have to turn them off again all the time. 
I think you need to select “Close” instead of “Start Over” on the ending screen, to enable fast mode. Once it’s enabled, you can restart the game without losing the option.
Unfortunately I can’t test this myself, since I can’t make the option go away, no matter what I do. If you would like to test it, the fastest way to kill Taylor is to immediately head for the peak and insist on climbing the rock.
Intuitive as all get-out. Not.
Yeah, the UI design could be better 
. Did you make it work, then?
Nope. I’m waiting to see if I get him killed again.
Hey, the app just got an update, and it surprised me to see some of the “fixes and improvements”…
Huh. That explains what happened to me, but every review I’ve read, and every comment from other people, led me to believe that they got Fast Mode after their first ending…
But, couldn’t I do that already? I could click on any node and it would rewind back to it. A great feature, incidently.