I would have to define the time period for the novel Freak the Mighty as taking place sometime between 1980 and 1993. The way that I came up with these dates in that the book was published in 1993 and I can see the cultural ideals of that time period being shown in the novel.
The novel does not include any reference to any specific historical happening. Freak makes reference to mythology and science-fiction, but it is not specific enough to set an absolute time.
My thoughts on why an author does not set a specific time period is that they risk the chance that a reader may not be able to relate to a novel if it takes place years prior to their existence. By not naming the time period, the author is able to let the action of the novel speak to the reader. Also, the action of the story is one which can be seen happening anywhere at, basically, anytime. It allows the novel to remain relevant throughout time.