Heard the epiphyseal plate of the long bones of short children closes too early. What might be the cause?

Not early - genes. We have a large number of growth plates throughout our body and the do follow a somewhat predictable schedule on their closure age. However, some children's will close a bit earlier than others and this is largely affected by genes and gender.
Two basic reasons. Most short kids have short parents and thus short person genes. Their genetic code tells their growth plates to close when they are short because that is when it is supposed to. Someone with excessive hormone production as an abnormality could push the plates to close earlier than expected.