I started a thread in this vein a few months ago, I think in this forum.
DD2 stopped napping at 18 months, when I stopped nursing.
She still doesn't nap. Now that she is 2-3/4 years old, she *may* nap at childcare, when her caregiver says it is naptime. I don't know why, but the caregiver says "lie down quietly" and she does. She won't do it with me.
I have also been giving her a homeopathic remedy to ease DD2's anxiety and nervous tension. It is the Hyland's product: Calms. I'm also trying Calms Forte, but I don't like it as much. Neither product gets DD2 to nap, but they do get her to calm down enough so that the whiny/terrible two days are quite so terrible.
For a while we could trick her into napping by taking her for a drive in the car, but she wisened up to that strategy... the Calms does help for that.
I feel that DD2 doesn't nap because of our family atmosphere: (1) I'm a pretty wound up person who doesn't nap --type A personality, and (2) we don't have much of a daily routine. ... I am somewhat powerless to change these things... she doesn't nap when I nap, and DH is not supportive of establishing a routine... you know the type: he prefers sponteneity and impetuousness.
Edited to add: DD2 does show signs of needing a nap, and is much happier if she has rested.