Welcome! Wish your little one's health state improves more each day so both of you can enjoy great days ahead!
On the forum you can find posts about great, wonderful, Down syndrom children who have progressed and learned a lot!
Here's a discussion where they say how many times a day do they do the lessons
http://forum.brillkids.com/parents-with-special-needs-children/down-syndrome-and-little-reader-program/, usually twice a day.
As for when to start, do it as soon as possible, and each time your child is happy.
Digg
