Why Do Our Eyes Close When We Fall Asleep?

Good question and the simple answer if that a great deal of effort is required for us to keep our eyes open. The small muscles of the eyes keep the lids open without realising they are working. However, when we get tired and sleepy, we relax the effort and our eyelids drop down because of the weight pulling on them.
In other words, we cannot sleep with our eyes open because we cannot hold our eyelids up whilst we are asleep.
There is also another reason why we close our eyes when we sleep and this is because the light from the outside would keep us awake by exciting our brain. So, when we want to sleep, one of the first things we need to do is to shut off anything that might make our brain want to stay awake and that includes visual images. This is why it is often easier for us to go straight to sleep when it is dark.