But he grew old—This knight so bold— (7-8)
The knight grows old. Perhaps, however, he's not just literally old, but also metaphorically old. In other words, maybe he's so fixated on Eldorado that he's prematurely aged. His fixation has created a sort of death-in-life.
And o'er his heart a shadowFell as he foundNo spot of groundThat looked like Eldorado. (9-12)
The "shadow" that falls over the knight's heart presages death. The shadows we meet later in the poem are even more closely linked to death. Here, it's almost like he's starting to die.
And, as his strength
Failed him at length,
He met a pilgrim shadow— (13-15)
The knight's strength "failed him." It sounds like the knight has just died, which explains why he meets a "pilgrim shadow." Just think of all the movies where somebody dies and then they meet a ghost right afterwards. The poem never really makes it clear whether the knight is dead or not, however.