Between the ages of 2 and 4, babies stop sucking their thumbs. Only 30% of babies continue sucking their thumbs after the age of one, according to a study by the University of Chicago. That means the majority of babies give up the habit before they turn one. Only 12 percent of infants still suck their thumbs after age four.  After the age of 4 old years, if the child continues to suck the thumb, consult a pediatrician. As the toddler is old enough to understand Instructions, counseling and corrective practices may help him or her break the habit.