In my opinion, the main theme of this poem is loss. The speaker has lost the love of his life and is going to be sad for the rest of his life.
I think that there are not a lot of ups and downs in this poem -- just one big up and one big down. The huge up is when they fall in love and she become his. He says their love is so great the angels are jealous of them.
But then she dies. And there surely cannot be much more of a down than that. So it's not exactly ups and downs of love. It's more like the "up" of being in love but then a big "down" of her dying.
Concerning Poe's "Annabel Lee," the enotes Study Guide on the poem lists three themes. I'll list them for you and give a brief explanation of each.
- Memory and Reminiscing: the "many and many years ago" suggests a great deal of time has elapsed since the speaker and Annabel Lee were in love. This is central to the poem, because fond memories are often idealized versions of the real thing. The speaker is probably not responding to an actual relationship, but to a false, inflated memory of the relationship.
- Death: the speaker is faced with having to make sense of the world after suffering a permanent loss. Notice that no natural cause is really given for her death--that would not be worthy of her. Instead, the angels were jealous of the couple's happiness, and killed her out of envy. The speaker attempts to make sense out of the randomness of disease.
- Class Conflict: the poem features conflicts of age vs youth, humans vs. angels, and the speaker against Annabel Lee's "high-born kinsman," who, it is assumed, don't let the speaker take part in the funeral, or even see or visit the body.