What the hell is up with Popeye always having one of his eyes closed all the time?

He’s missing an eye.

He’s Popeye the Sailor Man. Pretty sure it’s a pirate thing.

A quick examination of Popeye would reveal he suffers from bursitis, which has no effect on the eyes. My guess is he is nearsighted, and is just squinting.

He’s having a stroke.

Sailors squint. Being in the sun all day without protection ruins eyesight.

Smoke from his pipe gets in his eye.

Despite some mistaken characterizations over the years, Popeye is generally depicted as having only one blue eye, his left. In at least one Fleischer cartoon, Bluto refers to Popeye as a “one-eyed runt.” It has never been revealed specifically how Popeye lost his right eye, although he claims it was in “the mos’ arful battle” of his life. Later versions of the character had both eyes, with one of them merely being squinty, or “squinky” as he put it.

Source(s):
http://en.wikipedia.org/wiki/Popeye

He got spinach and jalapeno pepper seeds in it.

His brain has extensive physical damage, to the point that it can not process input from both eyes at once to create a 3d image without resulting in a lethal stroke.
If he opened his eyes, he would die.

Olive is a squirter…gagagagaga!

Popeye is actually a characterization of the Norse God, Odin. Also know as Odin-One-Eye. Odin sacrificed his own eye to gain knowledge.
It is also obvious that Bluto represents Loki, Olive-oyle, the goddess Lofn and, of course Wimpie is Baldr.,
All Popeye cartoons can be viewed as simplified graphic depictions of Norse (Aryan) Mythology put forth in an overly uncomplicated manner to introduce the illiterate US masses to the concept of a Master race. Aryan master race ideology was common throughout the educated and literate strata of the Western world until after World War II. Such theories were commonplace in early-20th century but understanding was well beyond the intellect of the basic United States television audience so it was decided to present them in a form more to their intellectual level; thus the cartoon format.

@rojo I never watchec the cartoons or ever saw any of the movies…but wow, that’s interesting…and kinda fucked.

@Symbeline yah, and (and in the interest of full disclosure) kinda bullshit too.

@rojo Still awesome, though. And I bet there’s some grad programs out there where you could write a paper making the connections, and it would be taken seriously.

according to the story, he lost it in the worst fight of his life.