There is no absolute certainty as to the specific disability that Menuchim has. It could, as your question indicates, be epilepsy, but this alone would not necessarily account for the child's inability to learn to speak and his motor difficulties. The doctor who comes to the house to give smallpox vaccinations says, "He will be an epileptic," while also claiming he can cure Menuchim at the hospital. We are also told that Menuchim has "attacks," which would support that diagnosis. Yet the child has another symptoms, including an evident deformity of the legs and, possibly, hydrocephalus—enlargement of the head due to water on the brain. Given the limited medical knowledge of the time and place and the parents' inability or unwillingness to obtain even the treatment that might have been available at the time, the exact nature or cause of Menuchim's disability is not made clear. His mother, Deborah, seeks help from a rabbi, who tells her that the child will become normal someday. It's not until many years later, when the family has immigrated to America, that this actually comes true. Menuchim, seemingly by a miracle, has grown up to be an accomplished musician and composer and is reunited with his now aged father, Mendel.
What the outcome suggests, if we are to attempt viewing it in clinical terms, is that Menuchim may be on the autism spectrum. Throughout history, there have been people diagnosed as "mentally retarded" who displayed extraordinary musical (or some other specialized) talent and were termed savants: this is the way such individuals were viewed at a time before autism, learning disabilities, and related conditions were understood. One's understanding of Menuchim's condition depends, perhaps, on one's willingness to see the story chiefly in spiritual terms, as in its eponymous biblical source, the book of Job. Mendel's faith, like Job's in Scripture, is in the end rewarded by God, and this is the miracle of his son's recovery.