I'm not exactly sure why, but my mother has the same problem. Our eyes use up a LOT of energy, though. I forgot the actual percentage, but it was a lot. So this may explain why when you read, your eyes feel strained and you get sleepy.
It may be due to weak eye sight, or may be you don't read in the right posture.
Because maybe you need glasses or you have been reading for a long period of time, so rest those beautiful eyes of yours.