The Demoness had been on the 2nd floor for quite some time, and she had made a name for herself in the entire Floor.
It was said that she could've ascended to the next floor whenever she wanted, but she didn't. And the only reason she didn't ascend was because of her obsession with the frozen tower.
Once she ascended, she would've stopped being a member of the City of Tides and lose the qualifications to enter the Frozen Tower, which she didn't want.
Before ascending she wanted to reach the fifth floor and maybe even go beyond. With each failure, her obsession increased. This became a knot in her heart, something that she couldn't get over without clearing the Frozen Tower.