Hello C.,
8 pm may be too late for her. Try putting her to bed at 7 pm and see if that makes a difference. It may sound counterintuitive but the reality is sleep begets sleep. I have twin girls who are 2 and the later I put them to bed, the earlier they get up .. the opposite is true as well. They also have better naps if they sleep longer at night. I think she's overtired and is having difficulty getting and staying asleep. Hope this helps.
R.
PS - I also just read some of the responses. My pediatrician said most children do not give up their naps (2 hrs. plus) until nearly 3, and that it's better for them to continue these naps as long as possible. I think you have to be consider your own child's needs. If the lack of a nap does not change her disposition, it probably means she doesn't need the sleep, but if, like you dais, she's tired, you may want to try to adjust her bedtime.