Okay it happen to me just now. I went to turn on the Fire and green light came on then went off and nothing but a black screen. Last time I checked earlier today it was at 64%. No apps running, WiFi off and asleep.
So I plugged it into the wall charger and the orange light came on. So I hit the power button and nothing. So I held it down for 20 seconds and it booted right up. Went into Settings\Device and it said the battery was at 0%
It's charging now and works fine now it's plugged into the wall but after that happening to me I suspect some kind of random software bug causing the battery to rapidly drain while sleeping.
This is very bad specially if you're not near your charger. Not to mention letting it go that far down is not good on the battery itself.