Hi, I'm going through a similar situation right now with my just turned 3 year old son, the difference is he didn't have a pacifier just decided he didn't want to nap anymore even though he used to love to nap. He's starting Pre-K soon so I was very flexible with him for almost 2 weeks and if he didn't want to nap after 15 minutes he could leave his room. Well when he didn't nap it was like someone switched my happy go-lucky child to a cranky, whiny, miserable child showing tantrums for the first time. Today was the first day I insisted he stay in his room for at least an hour. Yes, he was crying, yelling "no nap!" and beating on the door, but I stayed strong and made him stay in his room. After about 45 minutes he fell asleep and slept for 2 hours. When he awoke I had my pleasant and lovely son back. I would insist on the naps, children that age need the down time, they also are neurologically healthier when they sleep more. I read some kids with ADHD and behavioral problems have insufficient sleep. To be on the safe side keep trying to work the naps in or quiet time for at least an hour.
According to a great book "Healthy Sleep Habits, Happy Child" by Dr. Weissbluth, here are the stats: Mos. 13 to 15 - 1% have 3 naps, 43% have 2 naps, 56% have one nap. Mos. 16 to 21 - 23% have 2 naps, 77% have 1 nap at 18 mos.; 12% have 2 naps, 88% have 1 nap at 21 months. Mos. 21 to 36 - 5% have 2 naps and 95% have 1 nap at 24 mos.; 0% have 2 naps, 91% have one nap and 9% have no naps at 36 mos. On their third birthday, most children (91%) are still napping every day. At age 4, about 50% nap 5 days each week, and by age 5, about 25% are napping about 4 days each week. Naps are usually gone by age 6.
Hope this helps.
Bernie