I always read before sleeping. No matter if I go to bed at 11pm or 3am. I've never fallen asleep while reading, but it's very common to feel so sleepy that I just can't concentrate anymore and I have to turn off the reader before even finishing a chapter. Although I usually set a limit before starting reading: like read a chapter and then turn off the light. That limit is always broken, so that's why many times I don't finish a chapter.
But always wait for a text break before stoping.
If I read during day time, I don't fall asleep, but I feel somewhat sleepy. Maybe because reading so many times before sleeping induced my brain to think that reading time is always followed by sleeping time.