Yes, get him checked. If it won't close properly it usually indicates the start of an eye infection. Once an infection sets in blindness can come about without treatment in just a few days.
eyes might be dry. you could try some saline, like contact solution. if the kitty keeps it up i would take them to get checked.
I'm guessing you are referring to the nicotating membrane, an extra layer that cats have so they can "close" their eyes to protect them and still see. (Spooky, isn't it?)
When cats are nodding off or spacing, it isn't unusual to see the membrane partially closed--that's just carelessness on his part. But it wouldn't ordinarily be like that all the time; when he's alert, the membrane would be expected to disappear.