In the first three stanzas of "Eldorado," the speaker tells us that the knight has searched for this place for a really long time, but hasn't been able to find it. Bummer. That sure sounds like defeat to us. At the end of the poem, the shadow tells him what he must do, but this ends up just being another invitation to defeat. The poem isn't really about winning then, but about losing. The knight loses in part because he's looking for the wrong thing, but also because he doesn't ever give up—long after he should have thrown in the towel, raised the white flag, and called it a day.
Don't be a sore loser, Shmooper. Sometimes defeat is a good thing, because it makes us try even harder. The knight, after all, is still obsessed with finding Eldorado, even after he has been defeated numerous times.
The knight's quest for Eldorado is kind of ridiculous, which is why he is continually defeated in his search. He's a loser in many senses of the word.