The way Latin is taught even today would almost make one think that the language was bounded in space by Italy and in time by a period of just a few decades. As Jürgen Leonhardt points out, the classical era works form around 0.01% of the total written output of Latin, and the larger part of this book concerns the language's history in the post-Empire period.
Contrary to common opinion on the matter, Leonhardt asserts that the Renaissance humanists' attempt to return to Ciceronian purity was not the cause of the decline in Latin usage, as most Latin continued to be happily written without such strictures. However I'm not sure I understood any argument as to why Latin did subsequently decline as a communication medium if indeed he presented one - I found the author's arguments throughout often confusing and seemingly contradictory. It was fortunate however that the rise of classicism, historicism, philology and comparative linguistics and a belief that studying Latin was a way in itself of improving the individual ensured that it would remain as an integral part of education into modern times.
However the recent decline has come more than anything as a result of the obsession with the modern. Leonhardt warns that we are danger of losing people who can understand that 99.99% of Latin literature, most of which has never been translated or never properly studied, and thus losing access to much of our history. There are positive signs however with a resurge in interest in the language.