1. With only one exception I can think of, every instance of insomnia I've had in the last several years I can trace to not having f.lux enabled for some reason.
2. The reason that happens is that I often won't notice if f.lux dies for some reason, because I am so thoroughly used to it now.
I was having real sleep trouble several years ago, and f.lux is part of a battery of things I did (along with cutting caffeine completely after 12:00PM every day, getting some aerobic exercise, not coding after ~9:00PM, and taking over getting the kids out the door in the morning to force myself to get up) which more or less eliminated those problems.
Sure enough, I forgot to turn F.lux back on after disabling it for some photo editing on Sunday, so while I don't have any proof this seems like a strong correlation echo'd by all of the existing research on Herf's website.
I had onset insomnia: took me about an hour to fall asleep each night. I jailbroke my iPhone just to install f.lux.
Now I don't have onset insomnia.
If I wasn't clear: I can trace insomnia to f.lux being disabled; I'm not aware of it at the time, but then the next day or so I'm like, "oh, yeah, f.lux was off, shit." It's not like 11:30PM rolls around and I realize f.lux is off and suddenly I can't sleep.
See the f.lux webpages for some references.