And they haven't.
Affirmed's 1978 Triple Crown was the most recent in a sport that covets many more. So it is nicely coincidental that the 30th anniversary of Affirmed and Alydar's stretch duel in the Belmont is also the time when the long drought seems most likely to end.
See also, a New York Times column on steroid use in horses:
When you watch Big Brown at the Belmont Stakes, you will be watching a horse that is running on steroids. There is no denying the natural athleticism of Big Brown, who stands an excellent chance of becoming the first Triple Crown winner in 30 years. There is also no denying that it would be all the more impressive if it were not drug-enhanced.