Why do our eyes close when we sleep?
Our eyelids close when we sleep probably for the obvious reason that it prevents the sclera and cornea from drying out, becoming accidentally scratched (such as blowing dust) and allowing oxygen diffusion from the inside of the eyelid (to the sclera and cornea). Fragile corneas are a requirement for our vision. Thick corneas are much less fragile but then attenuates more light. 

From terdon:

1) blinking requires muscle movement which sort of defeats the purpose of resting 

2) closed eyelids offer much better protection than periodic blinking 

3) if you can blink, you have eyelids.