Clearly the chief way in which Titania's perseverance is demonstrated in this scene is through her conflict with Oberon and her refusal to yield the child that he desires so much. However, I would argue that this scene demonstrates her stubborness more than her perseverance. Whatever Oberon says, she is resolute in her refusal to yield this boy to him. Note how she responds immediately to Oberon when he brings up the subject:
Set your heart at rest.
The fairy land buys not the child of me.
She goes on to explain that she is bringing up the boy for the sake of his mother, who was a "vot'ress" of her order, and it is for "her sake" that she will nto part with him. Titania leaves after saying that she would not give Oberon the boy for his "fairy kingdom," reinforcing her resolute position and stubborn nature. The overwhelming sense we get of her character is that she is a determined woman who will not yield what her husband desires from her. Thus stubborness is perhaps more appropriate than perseverance.