Annabel Lee. He writes:

A wind blew out of a cloud, chilling
My beautiful Annabel Lee;
So that her highborn kinsmen came
And bore her away from me,
To shut her up in a sepulcher

These lines make it clear that Annabel Lee died. According to the Merriam-Webster dictionary, a sepulcher is “a place of burial” or a tomb. Poe even adds at the end of the poem discussing her burial site that Annabel Lee was placed,

In her sepulchre there by the sea—
In her tomb by the sounding sea.

However, in the poem Poe continues to say that the angels’ actions were fruitless. They could never extinguish a love as intense as the one he shared with Annabel Lee, which was deeper and stronger than people feel even if they are older and wiser than the two lovers described in the poem.

The poet says that his soul will never really be separated from Annabel Lee’s. He dreams about her every day. Whenever he sees the moon, he dreams about her. Whenever he sees the stars, he feels her beautiful eyes upon him. Thus, given his strong connection to Annabel Lee, which defies human senses, he lies down beside her side every night in her sepulcher or tomb by the sea.

According to the speaker of the poem, Annabel Lee died because "the winged seraphs of Heaven / Coveted" the "love that was more than love" felt by the speaker and Annabel Lee for one another (lines 9, 11-12). This is particularly interesting, I think, because we typically conceive of angels as being pure and virtuous. However, the speaker presents himself and Annabel as the innocent ones, saying, "I was a child and she was a child," and presents angels as covetous and really rather vicious (line 7). By suggesting that the angels purposely sent a wind from a cloud to chill Annabel, killing her, in order to separate the lovers, whose beautiful love they envied, the speaker paints these angels as rather cruel. They weren't "half so happy in Heaven" as the speaker and Annabel were on earth, and so the speaker claims that the angels sent a "wind [...] out of the cloud by night" to take her away (lines 20, 24). Not only that, but then Annabel's "highborn kinsmen came / And bore her [body] away from" the speaker, in order to bury her (line 17). However, he says, nothing "Can ever dissever [his] soul from the soul / Of the beautiful Annabel Lee" (line 32-33). In other words, despite the angels' best efforts to separate them, the souls of the speaker and Annabel are intertwined and can never be pulled apart, even if their bodies are not together.

The poem was written in 1849. 

The poem, "Annabel Lee" does not state directly how Annabel Lee died.  In the 3rd stanza the line, "Chilling my Annabel Lee", and the lines in the 4th stanza, ..... , chilling / And killing my Annabel Lee" might indicate that she died of influenza or pneumonia which would have been common in the 19th century. This is conjecture, of course, since the poem does not represent any one person in particular.  Many have speculated that the inspiration for the poem was Poe's young wife, Virginia Clemm, but she outlived Poe so her death was not an issue with him.

We do not know exactly how Annabel Lee died in this poem.

We are told two things that might be relevant.  First, we are told that a cold wind blew from a cloud and that was (it is implied) what killed Annabel Lee.  So from that, you could imagine that she might have died of pneumonia or of exposure (freezing to death).

However, if you look a little earlier in the poem, you see that it was angels from heaven ("winged seraphs") that caused Annabel Lee to die.  They were jealous of how perfect the love of Annabel Lee and the speaker was and so they killed her.

So you can pick which of these you want to use for the answer.  You can say the angels killed her or you can say she died because of the effects of the cold wind.

The speaker's reaction is certainly one of undying dedication. 

"Annabel Lee" can be read in the context of American Romanticism. It employs language to evoke mood and emotion; it uses elements of the supernatural (e.g., angels, winged seraphs of heaven, and demons) to illustrate the extraordinary nature of the narrator's love for the subject.

Because you are focused on the narrator's reaction, I would look to the last three stanzas. In the fourth stanza, we learn how Annabel Lee died: "That the wind came out of the cloud, chilling / And killing my Annabel Lee." Exposure to cold and dampness (she lives by the sea) was a concern in the 19th century. Perhaps it was pneumonia that took her. 

In the fifth stanza, the narrator expresses what was different about his love for Annabel Lee. They were spiritually connected spiritually long before her death: 

But our love it was stronger by far than the love
Of those who were older than we—
Of many far wiser than we—
And neither the angels in heaven above
Nor the demons down under the sea,
Can ever dissever my soul from the soul
Of the beautiful Annabel Lee:—

In the first three lines, you have the voice of a youth who believes that no one can understand the depth of his emotion, another characteristic of Romantic literature. For him, their love transcended age, and notions of good and evil. His evocation of demons and angels also suggests the possibility that their love transcended the boundaries of religion and the church.

In the final stanza, the narrator describes how Annabel Lee is present in his memory:

For the moon never beams without bringing me dreams
Of the beautiful Annabel Lee;
And the stars never rise but I see the bright eyes
Of the beautiful Annabel Lee;

She has thus become a part of everything in death. She belongs not only to the narrator, but to the universe. 

The last few lines are less spiritual. The poem becomes dark, even morbid:

And so, all the nighttide, I lie down by the side
Of my darling, my darling, my life and my bride,
In her sepulcher there by the sea—
In her tomb by the side of the sea.

Here, it seems that the narrator wishes to join her in death: He lies down by his "bride" in "her sepulcher," in "her tomb."

Depending on how one wishes to read the poem, this could be affirmative to Annabel Lee's memory: the speaker will never forget her. Or it could be dark: he is trying to climb into the grave with her. The latter reading would make it more explicitly Gothic, and much of Edgar Allen Poe's work is in the early American Gothic tradition.

The narrator's reaction can thus depend on one's choice of how to read the poem.

The speaker in "Annabel Lee" is distraught because his beloved Annabel Lee has died.

The poem begins with the speaker describing the incredible love that he and his beloved Annabel Lee once shared. He comments that he only thing Annabel Lee thought about when she was alive was how much she loved the speaker. They were young and shared a love that was so intense that it made the very angels in heaven jealous.

The speaker uses symbolism to first describe the way death snatched away Annabel Lee:

And this was the reason that, long ago,
In this kingdom by the sea,
A wind blew out of a cloud, chilling
My beautiful Annabel Lee;

This "wind" represents the force of death, and it "chilled" Annabel Lee—meaning that it took her life. This marks a definite shift in mood in the poem, and upon first reading this line, it may not be clear what this "wind" represents. The speaker follows this by commenting that "her highborn kinsmen came / and bore her away from me." These are Annabel Lee's relatives, and it seems that they have a higher social rank than the speaker does.

The next line solidifies Annabel Lee's fate:

To shut her up in a sepulchre

A sepulchre is a tomb. There can be no mistake at this point that Annabel Lee has died. At the end of the following stanza, the speaker returns to the symbolism of the wind as he comments,

That the wind came out of the cloud by night,
Chilling and killing my Annabel Lee.

The wind that "chilled" Annabel Lee is responsible for her death. Regardless of this loss, the speaker comments that his soul is so intertwined with that of Annabel Lee that they can never be fully separated. Thus, he lies by her tomb each night so that they can be together.

Like so many of Poe's poems, "Annabel Lee" concerns a speaker who bears love for a woman that is so profound that it nearly borders on obsession. The speaker and subject of this poem live in a "kingdom by the sea" and have a life that is described as being nearly perfect. The woman is shown to be more of an object than a functioning character. Her only desire in the world is to "love, and be loved" by the speaker. Halfway through the poem, the death of Annabel Lee is very subtly described. However, it leads to the intense misery of the speaker. He insists that they cannot be separated.

The exact nature of Annabel Lee's death is only vaguely elaborated upon, and is indeed given a romanticized explanation. This explanation is that "seraphs," or angels, in heaven saw the love between the speaker and Annabel Lee as so sublime that they became jealous. Vengeful angels sent a "chilling wind" to kill her and to, evidently more importantly, take her and her love away from the speaker. It is implied that "angels" may only be a placeholder for Annabel Lee's "highborn kinsmen" who likely also disproved of her attachment to the speaker. The poem is as much a proclamation of victory against those who would separate the speaker and his love as it is an ode to the subject of the poem herself.

The speaker begins the poem by recalling a time many years ago (like the beginning of a fairy tale) in a kingdom by the sea where he an a maiden named Annabel Lee lived and were in love. Although they were only children, their love was incredibly strong, so strong that angels were jealous of them: 

But we loved with a love that was more than love--
I and my ANNABEL LEE;
With a love that the winged seraphs of heaven
Coveted her and me. 

According to the speaker, the angels, in their jealousy, sent a wind from a "chilling cloud" which led to Annabel Lee's death. The narrator repeats this accusation, that the angels sent a wind to chill and kill Annabel Lee, evidently making her sick enough to die and she is carried by her family ("high-born kinsman") to her tomb or sepulchre. 

However, the narrator adds that their love was/is so strong that neither the angels nor the demons (nor death) could ever separate his and Annabel Lee's souls. After her death, he still sees/senses Annabel Lee in the moon beams, the stars, and the sea. 

In Edgar Allan Poe's poem "Annabel Lee," there are actually a few lines that convey the death of his beloved maiden whose only thought was to "love and be loved by" the speaker.

In stanza three, the tone shifts from one of adoration to a more somber reflection. In lines three and four in this stanza, he recalls,

A wind blew out of a cloud, chilling
My beautiful Annabel Lee;

So that her highborn kinsmen came And bore her away from me,