Is there a word to describe someone who keeps trying to do something but always fails?

The word you are looking for is SYSYPHEAN. Although rarely used it refers to the legend of Sysyphus, a man punished by the gods by attempting to roll a rock up a hill. No matter how he tried, the rock would roll back down the hill and he would be forced to start over. Used in a sentence it would be; Joe's many attempts at a business were sysyphean since they inevitably failed.

A few suggestions:

Loser. Literally someone who loses, but commonly used in a derogatory sense for someone who simply can't do anything right.

Schlemiel. Taken from Yiddish. A hapless person, one who always makes a mess of things.

Klutz. Also from Yiddish, meaning a clumsy person, a person prone to accidents and mishaps, so this would be a somewhat specialized case of what you are looking for.

Schlemazel. Yiddish again. An unlucky person; a habitual failure.

Bonehead. One who is lacking in cleverness; someone who can't "get a clue."

Failure. The literal representation of what you are looking for. A person who always fails.

Incompetent. Used in the noun form; one who has no ability to accomplish something.

And from a previous generation: Sad sack. This was the name of a cartoon character created in World War Two, and it became a term for the kind of person you are trying to characterize. Here's the definition found in The Free Dictionary (online): An inept person who makes mistakes despite good intentions.

I think of a bungler as a person who messes up pretty much everything he or she works on or touches.

n. One who bungles; a clumsy, awkward workman; one who performs without skill.

n. Someone who makes mistakes because of incompetence

To bungle is defined as:

To work or act in a clumsy, awkward, or blundering manner.

To make or mend clumsily; botch; manage awkwardly or blunderingly; perform inefficiently.

Born loser 1: a person or thing that loses especially consistently 2: a person who is incompetent or unable to succeed; also : something doomed to fail or disappoint

That's actually Merriam-Webster's definition of "loser", which I think has an even more negative connotation. A "born" loser just naturally fails at everything, while losers probably got that way through their own poor decisions. That's strictly my take, mind you.