Routine and schedules are important and that may be part of the problem. I think if you see that she's needing the sleep at her regular naptime, you might want to try different things to help her get to sleep. That way she will be able to stay up the extra hour and go to bed at her regular bedtime. It may sound mean, but we have one child in our daycare who sometimes needs us to just hold his hands and feet still until he settles down to sleep. He fidgets to try to stay awake even when his poor eyelids are drooping. Once we hold him still by gently, but firmly holding his feet in one hand and his hands in the other, he goes to sleep within about two minutes, and wakes 2 1/2 hours later rested and in a chipper mood. The trick is to help them lie still just long enough for the body to settle down and relax. Find what it takes for your daughter. It could be a back rub, simply putting on quiet relaxing music, or whatever. We've encountered kids who responded to having their fingers or their feet rubbed. Others liked the backs of their heads rubbed. For some simply sitting nearby and perhaps putting our hands on their chest would help. For others, just having us sit nearby was enough. I think one problem with non-nappers is that they may have a feeling of abandonment and not like being left alone. Just being nearby until they go to sleep may be the answer. You'll have to figure out what will work with your daughter. Now there are going to be times when nothing works, and she doesn't sleep at naptime, but at age three most kids who have had a reasonably active morning do need some rest around mid-day. On the days when she doesn't I would still keep her regular bedtime and see if that helps.