The Loisels did not leave the ball until about four o'clock in the morning because Mme. Loisel was having such a good time and had so many men wanting to dance with her. When she and her husband put on their outer garments, she was anxious to hurry away
...so that she should not be noticed by the other women putting on their costly furs.
She is a little like Cinderella, who loses a glass slipper in her haste to leave the ball before her coach turns back into a pumpkin.
Here Maupassant uses Mme. Loisel's vanity once again, but for a different purpose. It is almost certainly because she is in such a hurry to get away, and because it is so late and she and her husband are both tired, that she loses the diamond necklace. She may have tugged it off while she was pulling on her outer coat. But the necklace may not have fallen all the way down; it may have gotten shaken loose when they were "descending the staircase." She was not familiar with the feel of the necklace. She didn't notice it was missing until she had gotten all the way back to her home.
It seems a little unlikely that a woman could have a large diamond necklace fall off her neck and drop to the ground without her realizing it. Maupassant takes pains to make it plausible by describing their departure from the ball. They are in a hurry. They are tired. They are cold and shivering. She is probably clutching her coat tightly around her. They can't find a cab. They walk down the Seine "desperate and shivering." It takes them a long time to get home. She has no idea where she could have lost that necklace.
Maupassant specifies that the ball is held on January 18th. This is only to indicate that Mme. Loisel will be forced to wear her outer garments although she is ashamed of them. It is also because she has to wrap heavily in those outer garments that she is in a hurry to leave and that she runs the risk of accidentally pulling off the diamond necklace.