Many people look for a "cure" for autism, treating it as most diseases and disorders we meet in our daily existence – as something that we can defeat or simply "grow out of" in time. They spend a lot of money on herbal supplements, and "cures" that promise to "cure" a child of autism. Yes is autism something we can cure?
All autistic disorders are classified as pervasive developmental disorders (PDD), this means that it isn't something that's "curable". The official stance towards autism is that an autistic person will be autistic for the rest of their lives. This is because, among other things, because of the nature of autism. Autistic disorders are not caused by a lesion in the brain or by a disruption in the balance of neurotransmitters. The modern stance is that they are caused by different "wiring" of the brain, an uncommon pattern of neuroconnections which appears from birth.
Autism is a highly heritable disorders. It's heritability (which can be understood as genetic influence, the probability that an identical twin will have the same disorder) is higher than that of Schizophrenia and other biological disorders. Additionally it is unlikely autism is caused by any external factor, it is most likely a mutation which appeared during the early developmental period which happened in the mothers womb.
Of course we have to remember that this does not mean that the environment does not play a role, or that an individual with autism stays the same throughout their life. Like "neurotypicals" autistic people develop, and change through interaction with their environment and their experience during childhood will be different to their experience at an older age.
It might be useful to see autism as a pathway in life. There are definitely various unconventional obstacles on that path, especially in relation to interaction with other people, but this path, like any other can still lead to fulfillment and personal growth. It is just a bit harder.
So, in conclusion. The answer to the question "Can an autistic child simply grow out of it?" is a no. Autism is a biological disorder, and while there are many effective behavioral treatments that help in managing autism, autism is classified as a pervasive developmental disorder, which means that it will always will be there, and a child simply can't "grow out of it ". The best thing parents can do is to accept the fact, and instead of hopping a serious disorder will simply go away they would be far better of getting a proper diagnosis and help for their child as soon as possible.