well I don't typically let the battery run down...since it gives me sufficient time to plug it in...so, it's been so long since I let it run out, I really don't recall that it turned itself back on, but, I will admit, I could be wrong about that, if so, then, I'm assuming it simply would not be a function included in a beta iOS. (I recall letting my iPad (1) run out, but I do not recall it turning on by itself.)
In any case, my point is, just plug it in when the battery is low...you get notifications, you get red in the battery indicator in your status bar, the phone is telling you to plug it in, just don't let it run out, simple.
There is no reason to let the battery run out...these are not nickel-cadmium batteries that have the "memory effect" and need to be fully depleted and fully charged to last longer, they're lithium ion and that simply isn't the case.
Maybe you just need a car charger? Or an extension cord for those long nights of texting or gaming in your sleep?