Patient Soul

Monsters have been sealed in underneath Mt. Ebbot by a powerful spell, and seven human souls are required to break the barrier. Many years have passed since king Asgore declared all humans who fall into the Underground should be killed. King Asgore has captured five human souls. The soul of Patience, a definitely-not-overly-cautious eleven year old named Ashley, now holds the greatest amount of Determination in the Underground, granting the power to RESET to certain checkpoints in the Underground, even after she dies. But will Ashely have enough patience to withstand the repetitions of time?

In this AU's cannon:

Chara's soul trait is unknown.
The red Soul's Soul Trait is not Determination, Determination is an energy that allows one to persist after death, and the resolve to change fate, and no soul trait can correspond with it.
(SPOILERS)
for the sake of making things simpler, the red soul is Authenticity. I chose this, because "being yourself" is a common theme in Undertale, and this seemed the most fitting for the ball game's hint of you using all of the Soul Traits to some extent.
(END OF SPOILERS)
Every one of the soul trait children had the determination to reset, but ran out eventually (this was actually somewhat hinted at).

(SPOILERS BELOW)
*This one is a whole lot more BS than the others, but needed for the story* The red flag isn't any more special than the others, monsters just describe Authenticity in the winner's message in clearer wording, now.
Also, a small one, since in Undertale, you were able to get any flag color despite being the red Soul, it's the same for the other children.