What a good question! I don’t know the answer, but there must be some evolutionary reason for your eyes to have eyelids and your ears to only have horrible hairy bits to keep things out.
I would assume it would be something to with the fact your eyes are very easily (and permanently) damaged by very strong light/radiation, whereas your ears can stand a bit of noise (i.e. iPod headphones). But I may be wrong!
Your eyes and ears work with different kinds of sensor cells. Eyes take in light and do funky things with it to send the right kind of picture to your brain. And your ears use the motion of particles in the air to interpret sound waves and send those sounds to your brain.
Because your eyes can do things to the light before it gets to the sensor, like bend it (with your lens), or reduce it (with your iris), then the eye is a really complicated piece of machinery, that needs protecting from physical things like dust and pointy things. So while shutting your eyes also stops you seeing, it also protects the machinery
You ears don’t do anything with the sound waves or molecules, they just accept them, and the motion is necessary to hear something. Shutting your ears would shut out the sound, but would offer no particular protection, because the machinery is more rugged and is set well inside your head, so is less likely to be damaged.