You could try trimming it to get the dead weight off, that might spring the curls back up. Try long layers. However in some cases, that might not be the answer. Children's hair constantly changes...from growing/aging, hormones, any possible medications they take, etc...
Did you ever see a child with blond hair for most of their childhood and then as they get older, it gets darker? Kind of the same principal with the texture of hair.
No don't cut it, when I was a baby my hair was suuuper curly and platinum blonde until I got about 4 or 5 when my hair darkened to dark blonde and lost basically all of it's wave/curl until I turned about 12, there's nothing you can do to change the follicle shape around the hair that determines the type of hair your child has. My hair is very wavy and sometimes curly now and I'm 14. So just let your child's hair run it's natural course.
my grandaughter has my hair!
when i was young, mine to was very light blonde, but as ive aged, its got darker, ashy, and thiner too..
if i just wash her hair, i let it air dry, that way, nature will do its job..
on mine, i dont do to much!
if i blow dry it, its more thin, but lightly dry it, the curl comes back more..