This happens when Scrooge is visited by the Ghost of Christmas Past. In stave 2, Scrooge returns to a younger version of himself, and Belle is there. Her eyes are wet with tears, and she tells him that an "idol" has replaced her—a "golden" one. She accuses Scrooge of allowing all of his other hopes to fall away until the "gain" of more wealth has completely encompassed him. Scrooge says that he has "grown wiser" in this but that he hasn't forgotten Belle.
Belle tells him that their engagement was made when they were both poor and then asks him:
If this had never been between us ... tell me, would you seek me out and try to win me now?
Sadly, Scrooge doesn't answer in the affirmative. He could have at this point declared his faithful love to Belle and told her that he needs her in his life. Instead, he simply answers, "You think not."
Belle goes on to tell Scrooge that if he married her, he would look at her with regret in the future, so she is therefore breaking off their engagement. Scrooge looks at her like he wants to say something—and then stops.
Belle leaves, telling Scrooge that she is sure he will be glad that he awoke from this "unprofitable dream," and he watches her go without saying anything to the contrary. He doesn't deny any of it.
Because Belle doesn't come from money herself and because Scrooge has become engrossed in the acquisition of more and more wealth, Belle is not important enough for Scrooge to keep in his life.