Toddlers at this age, tend to protest napping. And they are experts at forcing themselves awake. Then, when they are actually "over-tired" they will actually seem so "wired" and keyed up... that mistakenly others will think they are too "awake" to sleep. But in actuality, they are just over-tired. Over tired kids will actually get more "hyper" many times.
It is not that they are "giving up" a nap and therefore don't need one, but they are getting so independent, want to keep playing, and don't want to. And at this age, they are changing so much in so many ways.
BUT, at this age, naps are still important... even in preschool and Kindergarten, there are nap times for the children. Napping or getting enough sleep, aides in their brain growth, and immune system too, among other things. It is beneficial.
At this age, if she does not want to go down or actually fall asleep... it's best to have a "quiet time." If she is and can just stay in her place, and sing/talk to her stuffed animals etc. and entertain herself quietly, then fine. I know it cuts into her "nap" time... but, at least she is in her bed doing this and having quiet time.
In tandem with this, still keep to a regular nap time, everyday... or quiet time. Keep the routine the same everyday. Consistency is important. In time, she will get back to regularity. This is a hiccup in her nap habits for now... but she can get back to it. About 1/2 hour before you want her to nap, give her a verbal "warning" that nap time is coming up. Toddlers don't like having a "shock" being told all of a sudden in the middle of something that NOW they have to nap. Let her know in an encouraging way, that nap time is coming up. Then put away the toys, change into jammies or what not, go pee/change diaper, darken the room or house, and then lead her into her room or bed, or where ever she sleeps.
I have done this with both my children. Both my children ( 5 yrs. old and 24 months old), STILL nap, everyday. My youngest naps twice a day, my eldest naps afterschool. Sure, there were days when they didn't "need" a nap... and so on those days, I still kept a quiet time, at the same time, everyday. But first seeing if they would nap.
Another method I did, when my girl was that age, was telling her it was MY nap time, that MOMMY was going to nap. Then I would go about "getting ready", plunk myself down on the couch, tell her to come by me, put some toys next to me for her to "play" with, then shut my eyes. Reverse psychology. Sure, I would keep my eyes and ears "open" and watch her. But at the same time, I could lie down, and "rest." It worked many times. I would also tell her to "help Mommy" and let me rest etc.... and she felt she was then HELPING me... and would feel all proud "letting" Mommy "rest." (wink).
But in time, my kids, throughout their growth changes and development... have still maintained a regular nap habit. And they still go to bed fine at night. It is because i have, still everyday, kept to the same routine of napping and/or quiet time and my not giving up, and keeping to the same pattern.
Sure, some kids just don't need a nap...but, it's more of the fact that they don't want to, "seem" fine staying awake, and then the parent letting go of naps, because it takes so much effort to get them back to napping. So then the child ends up not napping and being "allowed" to stay awake. So the child gets used to that.
But at this age, it is a phase. If you keep up regular habits, you can still manage a "nap" or quiet time, at a certain time of the day. Then many times, in the midst of a "quiet time" the child will fall asleep. Kids also need to wind-down first... before napping. Otherwise they are still to wired to go down.
I believe it is a phase. As I have gone through that with both my children. At this age, it is a fork-in-the-road as far as napping...(1) you either disregard napping at this point in time... and let it go. Or, (2) you still nurture a "habit" of napping and/or quiet time...but it takes patience and consistency. Everyday. For myself, I chose the 2nd choice. My kids still nap even this day. They are napping now as a matter of fact. But that is just me. I know it's not easy getting kids to nap... but somehow, I have managed this habit with my kids. My daughter will even say she likes to nap when she is tired. My son, if he is tired, will even take my hand and lead me to his crib.
Everybody is different. Decide what is best for you and the whole situation. If she were in preschool/daycare etc., they would be having the children nap.
Good luck,
Susan