Answer by Steven Fowkes:

One person I know with DS has an IQ equal to mine. She became a veterinarian.
So yes.
All you have to do is preserve the beneficially wired neurons in the fetal brain during the pruning phase of infant development, which is from birth to two years of age. In DS, elevated levels of hydrogen peroxide from over-expressed SOD-1 on the 21st chromosome causes excessive apoptosis. This begins when infants are born and start breathing air for the first time. So if you start at birth and keep the peroxide-scavenging systems at full induction, the over-pruning of brain neurons following birth is normalized and IQ is preserved.  This involves preventing both iron and selenium insufficiencies. Iron is the cofactor for catalase. Selenium is the cofactor for glutathione peroxidase. If iron and selenium are not insufficient, catalase and glutathione peroxidase induction is optimized. This prevents the vast majority of brain over-pruning and normalizes IQ such that the second and third standard deviation on the IQ curve is still well populated.
A deeper and longer explanation can be found in the Down's Syndrome Collection, an 85-page free PFD download at Project Wellbeing (on the "Steve" page).

Can people with Down's syndrome have a high IQ? Explain.