The engines used in most small aircraft are basically unchanged since the 1950s or 60s. Aircraft are required to have regular maintenance, including major overhauls, so while these engines are archaic in terms of technology they keep running fine and have a track record of reliability. Newer designs would have to be certified by the FAA, which is apparently an extremely expensive process. General aviation is already so expensive that it's inaccessible to most people, so no one really wants to push the price tag up even more.