Gatsby's dream was unattainable because it didn't really exist. He was in love with a memory, and he eventually realized that Daisy was not the woman he fell in love with (maybe she never was). The brief affair ended because Daisy would never have given up social position for a man who couldn't ever really fit into her world.
Gradesaver explains this beautifully in their Chapter Five analysis;
This chapter presents Gatsby as a man who cannot help but live in the past: he longs to stop time, as though he and Daisy had never been separated and as though she had never left him to marry Tom. During their meeting, Nick remarks that he is acting like "a little boy." In Daisy's presence, Gatsby loses his usual debonair manner and behaves like any awkward young man in love. Gatsby himself is regressing, as though he were still a shy young soldier in love with a privileged debutante.
Nick describes the restless Gatsby as "running down like an over-wound clock." It is significant that Gatsby, in his nervousness about whether Daisy's feelings toward him have changed, knocks over Nick's clock: this signifies both Gatsby's consuming desire to stop time and his inability to do so.
Daisy, too, ceases to play the part of a world-weary sophisticate upon her reunion with Gatsby. She weeps when he shows her his collection of sumptuous English shirts, and seems genuinely overjoyed at his success. In short, Gatsby transforms her; she becomes almost human. Daisy is more sympathetic in this chapter than she is at any other point in the novel.
The song "Ain't We Got Fun" is significant for a number of reasons. The opening lyrics ("In the morning/ In the evening/ Ain't we got fun") imply a carefree spontaneity that stands in stark contrast to the tightly-controlled quality of the lovers' reunion. This contrast is further sharpened by the words of the next verse, which run: "Got no money/ But oh, honey/ Ain't we got fun!" It is bitterly ironic that Gatsby and Daisy should reunite to the strains of this song, given the fact that she rejected him because of his poverty.
