Why does the narrator repeat in the story "on a tarnished gilt easel before the fireplace stood a crayon portrait of Miss Emily's father"?
The image of Emily's father behind her in crayon on "a tarnished gilt easel" suggests the patriarchal society in which Emily has lived; it is an antiquainted one, at that, signified by the tarnish on the gilt. The word gilt also suggests wealth as in "The Gilded Age" at the turn of the 20th century. That the portrait is done in crayon, a word that suggests childhood, indicates that the portrait has long been hanging in the house of Emily's father; and, even though Emily's father is dead, he still wields his power over her. Clearly, this portrait is a symbol, and, as such, it is repeated in order to signify that the father and the genteel Southern life yet influences Miss Emily.
Along with the theme of the Old South, the theme of death is as prevalent as the mention of the portrait. As Emly stands before the portrait of the father who is dead, Emily herself appears death-like:
She looked bloated, like a body long submerged in motionless water.
Her house, long closed with the "only sign of life about the place" being the old "Negro man," retains the portrait still hanging. Perhaps Emily's standing before the painting is symbolic of her "clinging to that which had robbed her," all the young men who had called upon her.
The previous answer to the question was extremely helpful, but it contains possible misleading information about the nature of the "crayon portrait." After doing some additional research, the "crayon portrait" which today indicates childhood absolutely did not during the discourse time of the story. According to Florida Memories (State Libraries and Archives) a crayon portrait is a "weak photographic image printed by a developing-out process and finished by applying charcoal or pastels giving the appearance of a painting." Portraits such as these were common from 1840 through about 1915. I have seen many of these crayon portraits in antique shops across the country. The subjects of these portraits are particularly spooky looking. It would add just the right touch of the macabre to the room.