What if the universe only functions when watched by an intelligent observer?
What if changes in state (or motion) are a function of those observer's perception? The Schrödinger's cat thought experiment seems to imply that that might actually be the case. And if it is, how would we ever know? We cannot know a thing until we look at the thing, so if our looking influences the results, we are skewing the results every time we inspect them.
Now in this perception dependent universe, all a person would have to do to stop time, is diminish the authority of everyone-else's perception to a level beneath the intellectual threshold which insights motion. Once this is somehow done, your unstopped/undiminished heroine can enjoy the godlike power of being the only animating force in the universe. What she sees or interacts with, functions normally; Balls that she kicks, roll while she watches them. Sunshine strikes her face because she believes it should. Air molecules move out of her way, because not moving would defy her expectations. Meanwhile, all around her, the rest of the universe remain static and unchanging, just as all the gold-watch stories which she's read, suggest that it should.
Other people are a bit of a challenge to this answer. The classic time-stop scenario has other people standing around like Mannequins. But if motion in the universe is driven by your heroine's perceptions and expectations, then the people she sees should re-animate as she looks at them.
So what if her gaze does reanimates other people's bodies, but not their minds, not their motivating source. If she looks at someone who was falling, they would continue to fall. But if prior to the time-freeze, she hadn't seen them falling, they would just stay where they were, with no new motion starting from within them. Similarly, non-falling people would be technically animate, but un-moving because their minds, which the heroine cannot understand or predict, remain frozen with time. They might even have a heartbeat and blood pressure, but no will of their own.
This opens up some interesting plot opportunities involving intimacy and love. If she looks deeply into a frozen person's eyes, she might be able to see their souls like a frozen fire; and in seeing them in this way, come to understand them, at least well enough to reanimate the minds. Such people would become alive in the frozen world, at least until she looks away.
Similarly, people, whom the heroine already knows closely and/or loves, might be immune to the time-freeze, since her knowledge of them is a permanent part of her perception and understanding of the world. She might find that she is not as alone in this static reality, as the stories suggest that she should be.
-- this is a heavily edited version of my original answer which included some scientific assertions which didn't survive peer-review. --