The other answers to this question are correct in that the last liberal arts college was shut down 40 years before the events of the book because no one wanted to go to such a college or help fund such a college. However, it might be helpful to think about why this matters in the context of the book.
Liberal arts colleges are colleges that teach students a wide variety of subjects. They can be distinguished from colleges that are more concerned with teaching technical subjects or subjects that are clearly meant to make it easier for the students to find jobs. Liberal arts colleges are meant more for those people who want their minds enriched and who want to learn to think. This is the very antithesis of what the society in Fahrenheit 451 wants. That society does not want people to think at all. Therefore, it would discourage anyone from attending a liberal arts college.
This is why the closing of liberal arts colleges is relevant to this book.
In Part II of Fahrenheit 451, "The Sieve and the Sand," Montag learns that the last liberal arts college was shut down 40 years before. Faber had taught at this college, but he lost his job when the college was closed because it lacked patronage and students. Faber says, "I don't talk things, sir...I talk the meaning of things" (page numbers vary by edition), and he is also able to recite poetry. Montag consults his files, and he learns that Faber is the subject of "future investigations."
Faber's ways of thinking and being are very different than those of the other people in Montag's society. Montag eventually turns to Faber to help him feel less numb and to learn about literature. Faber knows what the society was like in the days when people read books, and he can help Montag connect to the world of thought and reading.
In the section entitled "The Sieve and the Sand", Montag tells us that it was “forty years ago when the last liberal arts college shut for lack of students and patronage.” This means forty years prior to the start of the story. The year of the story is not specified, but it is sometime in the 21st century.
IN the book it states 40 years ago!
40 years ago
forty years ago when the last liberal arts college shut for lack of students and patronage.