This study identifies one particular group of autistic children that tend to make great strides:

One group of ∼10% of children experienced rapid gains, moving from severely affected to high functioning. Socioeconomic factors were correlated with trajectory outcomes; children with non-Hispanic, white, well-educated mothers were more likely to be high functioning, and minority children with less-educated mothers or intellectual disabilities were very unlikely to experience rapid gains.

via Six Developmental Trajectories Characterize Children With Autism.

The authors speculate that the group they call “bloomers” (start out LF and improve dramatically to HF)  may get better services, have parents who are better able to advocate for their children, and have well-educated mothers who more likely to be able to stay home and coordinate the autistic child’s care. This study did not take into account treatment the children received; so the relationship between socioeconomic status and “blooming,” while clear, needs to be clarified by more specific data about treatment in these groups.