My DD was always a terrible napper. When she was an infant she would take 2 one hour naps a day & sleep about 10-12 hours a night. From 15-30 months we got one 1.5 hour nap on weekdays. From 30-31 months they could get about 30-45 minutes 3-4 days a week at preschool that she fought HARD. That's when we gave up & told them at preschool to just give her "quiet time". During quiet time at school she can read (we used to send her TAG in with headphones) or do puzzles by herself. At home, she plays quietly in her room, usually reading or having "picnics" with her dolls.
Now, at 48 months She sleeps about 8-10 hours at night (she prefers to stay up reading & will sometimes pretend to be asleep & then be caught 2 hours after bedtime -- she's a girl after my own heart). The only time she naps is if we take a long car ride (2+ hours) or if she is sick, she'll put herself down for a nap.
I can only assume it's genetic at this level of sleep since I also was not a napper as a child & even now I only sleep 5-6 hours a night! I hope that helps! Our free time is from 8:30 (when we put her to bed) and 12AM!
