My son started doing something very similar a few months before his third birthday. Several days he would sit in his bed and play for the entire nap period. On those days he would fall asleep at nighttime earlier than usual, but not significantly. This was during the same period of time that he attended preschool in the mornings for a short time. On the days that he had preschool, he had trouble napping when we got home, and on some other days, too. He is now back to sleeping regularly at naptime and has even extended the amount of time he sleeps (he is 3 yrs 4 mos). I have a couple of theories about the irregular naptime behavior.
On the preschool days, I have a feeling that he might have been "overstimulated" or something like that. I picked him up from preschool just as he was finishing lunch, then we would go straight home and down for nap (that was our usual routine to have naptime right after lunch). On other days, if we were out and about and arrived home just before naptime, he also had trouble sleeping. I think he needed to have a little down time at home before taking his nap. A peaceful lunch at home, then nap. When I made an effort to be sure we were home for lunch, maybe that helped him to prepare mentally for the next step - naptime - because he would go right to sleep.
On other days, if we had an inactive morning, he would also have trouble sleeping and just play for his entire nap period. For those occassions, I felt he was not getting enough activity and therefore was not tired enough. He is an active, energetic little boy, so I don't have to make too much effort to be sure he gets enough activity. But I found that if he has some good activity in the morning, then we settle down for lunch, he naps well.
These seemed to be the issues for my boy. If there is something that is actually hindering your daughter's naps, it may be different. I can remember taking naps in Kindergarten, so I always expected that I would be sure my children had naps until they were in school. If they outgrow the need for a nap before then, I still plan to have "quiet time" (we'll see how my "plan" works!). I do think that having a period of quiet rest during the day is beneficial at any age. If they don't actually need to sleep, that is fine, but they do need to take a break (and mom needs it too!)