Maybe people who grew up during the Great Depression had less opportunities? Or maybe baby boomers born right after the war overcame the silent generation in influence by numbers.
I think we're starting to see a similar phenomenon with Generation X being pushed out by long-lived Boomers and even a couple of Silents, but at least we had Obama (born 1961, so he barely counts) in between Boomers.
With that said, it's not for lack of trying that we haven't had a Silent president. Aside from the aforementioned Mondale and Kennedy's attempt, we've also had Michael Dukakis and John McCain as major-party nominees, the only third-party candidate who had a chance in Ross Perot, plus Bernie Sanders was a major contender and runner-up for the Democratic nomination twice.