In Fahrenheit 451, when was the last liberal arts college shut down?

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.