Had journeyed long,Singing a song,In search of Eldorado. (4-6)
The phrase "in search of Eldorado" is interesting. It sounds like the knight's search is still ongoing, which is another way of saying he still hasn't succeeded. He hasn't been defeated yet, but then again he hasn't won either. He's in between.
And o'er his heart a shadowFell as he foundNo spot of groundThat looked like Eldorado. (9-12)
The knight hasn't found anything that even looks like Eldorado. His whole search has been one giant defeat. The rhyme on "Eldorado" and "shadow" suggests that he will never succeed, a point emphasized in the final stanza when the shadow basically tells him to ride to his death if he "seeks for Eldorado" (24).
"Over the mountainsOf the Moon,Down the Valley of the Shadow,Ride, boldly ride," (19-22)
The shadow encourages the knight to keep looking, only it sounds like he's encouraging him to go ahead and ride to his death. To die and not find Eldorado is to be defeated yet again. It almost seems like the only thing that comes of the search for Eldorado is defeat.