Another oddball view of the facts, one that my particular chronological exposure to the Oscars may make more obvious.
I first watched the Oscars at the 1962 show, and became my obsessed self about the time of the 1965-66 awards. In those first five years, I saw David Lean, Robert Wise and Fred Zinnemann win second Oscars for directing. This was not an unusual occurrence at that time. In the 39 years of the Oscars though 1966, 30 of the 39 directing wins had been by people who won more than once (covering 13 directors, Capra and Wyler having won three times and Ford four). This compared to only 9 wins by one-timers. And even most of the one-timers had at least managed multiple nominations -- over that entire 39 year span, only four men (Norman Taurog, Victor Fleming, Delbert Mann and Tony Richardson) won on their sole shot.
But that tradition/history/whatever you call it came to a sudden stop, as if someone had drawn a red line, after 1966. Over the next 17 years, I watched 17 different people named best director. Many of them achieved multiple nominations over the period, and some, at least, seemed like they COULD have won more than once (Nichols, Coppola, Allen), but the fact is, no one did. Also, during that stretch, more people won on their one-and-only nomination than had in that earlier, twice-as-long period: Franklin Schaffner, John G. Avildsen, Michael Cimino, Richard Attenborough and James L. Brooks (it pains me to include Brooks with these lesser lights, since he was expected to be -- and should have been -- a second-time nominee for Broadcast News, but stats are stats).
And then, the tide shifted again. Milos Forman -- whose first win had come in the middle of that 17-year stretch -- broke the streak by winning his second for Amadeus (the fact that four of that year's five directing nominees were former winners had made a repeat a statistical likelihood). And since then, multiple winners have once again become a regular thing: Oliver Stone, Clint Eastwood, Steven Spielberg, Ang Lee, Alejandro G. Innaritu, and, now, Alfonso Cuaron, have all won twice in the 34 years since Forman's second win. One-and-done syndrome also appears to have waned some -- between 1983 and 2007, only five people have achieved that distinction: Kevin Costner, Jonathan Demme, Robert Zemeckis, Anthony Minghella and Sam Mendes. (I cut off after 2007 because it's too recent, and we're too early in some directors' careers to know if they might repeat. It's easy to imagine Boyle, Bigelow and Chazelle, minimally, making return appearances. Not to mention Mendes. Remember: even Mel Gibson got a years-later second nomination.)
I don't know that all this means anything, but it's a statistical anomaly that caught my eye.