One response that many linguists might endorse would be that language structures vary fairly randomly over centuries, so if the early languages you know about happen to have a lot of inflexion, the most likely direction for them to move has to be less inflexion (whereas if they had happened to have unusually little, a shift towards more inflexion would be likely – arguably the history of Chinese would fit the latter pattern). However, some linguists these days would say that one can be a bit more sophisticated than this about predicting directions of structural modification. A leading figure here is Peter Trudgill. He argues that language structure is heavily influenced by whether the language in question is that of a closed community, not often acquired by outsiders, or on the contrary is a "world language" used by many people whose first mother tongue was different. In the former case, the language can develop all kinds of structural complexity, which is maintained because the only people using the language are people who are soaked in it from birth onwards. In the latter case, many complications will be eroded because foreigners acquiring the language don't have time or perhaps enough motivation to master all the little curlicues. As Rome morphed from a city-state into the centre of an enormous empire, Latin came to be a "lingua franca" used over wide areas which had previously spoken quite different languages – the territory we now call France, for instance, became Latin-speaking, and peoples on the edge of the Empire often used Latin for external communication even if they retained their native languages. Similar things happened in the Eastern Mediterranean with Greek, which came to be used by many people as the language of civilization though their own languages were often not even Indo-European. (Consider e.g. the fact that the New Testament was originally written in Greek, to give it wide circulation, though many of the people to whom it was addressed, and I think some of the writers too, were not native Greek speakers.) And sure enough, in the post-Classical centuries, the Romance languages which developed out of Latin, and Modern Greek, all became inflectionally simpler than the classical languages.
If you should be interested in pursuing these ideas further, one publication that might interest you is a book edited by myself, David Gil, and Peter Trudgill, "Language complexity as an evolving variable", published by Oxford Univ. Press in 2009. Some chapters are rather technical, but others are quite accessible to people with no technical background in linguistics.