It is unclear precisely why the Mariner's curse is broken after he blesses the water snakes. To answer this, we ought to consider why the Mariner is punished in the first place.

Essentially, the Mariner is punished because he shows a lack of respect towards nature and therefore a lack of respect towards God. If the Mariner had valued the albatross as part of God's creation, he would not have killed it in such a nonchalant manner.

As such, the Mariner is arguably cursed because his killing of the Albatross signals an attitude of superiority and apathy towards the natural world, which in turn revealed his disrespect towards God. It therefore follows that when Mariner is finally able to appreciate the inherent beauty of value of God's creation, as evidenced by his appreciation of the water snakes, he is relieved of his curse.

This act of appreciation shows that the Mariner has learned from his past mistakes and finally understands that he destroyed something beautiful and inherently valuable.

It also must be considered that the Mariner does not come out unpunished after his misadventure. Although the curse of the albatross around his neck is broken, the Mariner is still cursed in the sense that he is compelled to tell his story to anyone who might need to hear it, including the wedding guest.

The Mariner does break his curse in a sense, but he still must endure the consequences of killing the innocent albatross. We might therefore conclude that the Mariner never truly breaks the curse.

In "The Rime of the Ancient Mariner," the eponymous mariner recounts how he killed an albatross that had supposedly brought good luck to his ship and fellow mariners. For killing the albatross, the mariner was cursed.

In part 3 of the poem, the mariner describes how all of his fellow mariners died suddenly. He says that as he watched all of his fellow mariners die, each "cursed [him] with his eye." The "curse" that he saw in their eyes was their individual curses for him, as he was the man who, by killing the albatross, had caused the ill-fortune that, in turn, resulted in their deaths. At the same time, the "curse" he saw in their eyes was the curse that he took on when he killed the albatross.

As he watched his companions die, the mariner understood that he "could not die." He says that while all the men around him died, "a thousand thousand slimy things / Lived on; and so did I." The mariner's curse is thus to survive his fellow mariners and to live on feeling, relative to the men he watches die, like a "slimy thing." He is cursed to watch everybody else die and to spend the ensuing days utterly alone, surrounded by death. He is cursed to be "Alone, alone, all, all alone, / Alone on a wide wide sea!"

In the seventh and final part of the poem, the mariner also reveals another aspect of his experience that could be considered a curse: he is compelled to journey "from land to land" to tell his cautionary tale to people he meets. From time to time, he says, he is beset with "a woeful agony, / Which force[s] [him] to begin [his] tale." In these moments, he also has a "strange power of speech" that enables him to speak forcefully and eloquently, to better convey his warning to those he meets. The "agony," he says, "within [him] burns" until he has told his tale once more.

Thus, the mariner is cursed to forever wander the world, "from land to land," retelling his cautionary tale over and over, and, at the same time, reliving his own harrowing experiences over and over.

The curse cannot die, because the Mariner must retell his story in an attempt to teach others about the dangers of impulsive sinning.  When the Mariner sinned, it was on impulse and for his benefit--his motives were purely selfish.  Thus, his chance for salvation was destroyed, dooming him to an eternal living death.  His soul can never be free from its sin.  However, each time he retells his story to an attentive listener, he comes one step closer to the atonement needed for true salvation.  The ultimate question Coleridge leaves us is whether that atonement can ever truly be performed.

The curse is a constant reminder for the mariner that he a)caused the deaths of his crew and that he b)committed a horrible act by disrespecting nature and the albatross that is a part of nature by killing it.  He must tell his story so that he never forgets the severity of what he did.

The very nature of the curse is that the Mariner must retell his story time and again so that others faced with a situation like his, will choose differently.  I do believe that the Mariner gets some personal redemption each time he tells his story if the person who he is telling stays and listens.  By the end of the story, the curse is more of a mission.

The answer to this question can be found at the very end of Part I and is reinforced at the beginning of Part II. At the end of Part I of this excellent ballad, the Ancient Mariner tells the Wedding Guest that he "shot the albatross," which was the catalyst that triggered off his subsequent disasters. Consider the following stanzas from the beginning of Part II and the way that they immediately indicate that something has gone very wrong indeed:

And I had done a hellish thing,
And it would work 'em woe:
For all averred, I had killed the bird
That made the breeze to blow.
Ah wretch! said they, the bird to slay,
That made the breeze to blow!

It is therefore the Mariner's act of unthinkingly killing the albatross that causes the deadly predicament that both he and his fellow sailors face. It is this act that has so offended the "polar spirit" that nature itself, personified in this form, takes his revenge on not just the Mariner, but all of his fellow sailors as well.

The Mariner tells the Wedding-Guest about the deaths of the two hundred other sailors aboard his ship—the entire crew except for him. After he kills the albatross, he brings a curse upon himself the and ship, and the men die. For a week, they are dead at this feet and all around him, but they do not "rot" or "reek." However, the look in their dead eyes torments him. He says it has "never passed away" from his memory. He calls it more "horrible" than an "orphan's curse," stating,

Seven days, seven nights, I saw that curse,
And yet I could not die.