In Foundation, Seldon apparently uses psychohistory to predict the actions of individuals, something that is deemed impossible in the prequel novels. However, the reader only sees Seldon perform psychohistory once — when predicting the ruin of Trantor. In all other cases, we simply are taking Seldon's word for it. The explanation: despite what he told the viewpoint character, Seldon is lying when he claims to have predicted the actions of individuals; in some cases, he actually engineered these events with the help of his mentalists.
Alternately, he's not using psychohistory to predict such events as his own arrest or potential execution, but plain old-fashioned sociology. No hyper-advanced math required, just a realistic grasp of current Imperial politics, plus some basic probability knowledge, e.g. how likely he'd be to get a Hanging Judge who'd want him dead rather than exiled.
A number of Zeerusty aspects of the series - aging rulers who suffer illnesses no one can cure anymore, the Mule's deformities not having been corrected surgically long ago, agricultural practices so crude that a large peasant underclass is required and it takes 20 farm-worlds to feed Trantor - make more sense if you consider that even Seldon himself only acted to preserve A) the physical sciences [First Foundation] and B) the mental/social ones [Second Foundation]. Somewhere along the way, either before the Empire's rise or early in its decline, the life sciences seem to have fallen by the wayside, long before Seldon had a chance to preserve them.
The regression of life sciences may actually have been one of the factors that convinced Seldon that the Empire in decline even before he developed the math for psychohistory. Even a casual examination reveals that the Empire relied on it's effectively limitless resources to address most problems rather than aiming for efficiency. The huge population of Trantor, and the Empire overall, could have led to a We Have Reserves mentality causing the government to reduce support for such sciences. Plus, as in any monarchy, there are likely to be heirs who want the current emperor to die so that they can ascend the throne. Such a culture might deliberately undermine the medical sciences in particular.
Another contributing factor might be the sheer longevity of the Galactic Empire and the extent to which it seems to have terraformed most planets. While there's still interesting game to hunt on some of the fringe worlds like Anacreon, we rarely get much mention of exotic biology on those worlds, or of organisms or diseases capable of threatening humans or even their favored crops. If the Empire reached a height at which most infectious diseases could be isolated and cured, and mastery of xenobiology was no longer required because virtually the entire galaxy had been surveyed, mastered, and cleared of any hazardous life, then the perceived need for the life sciences might fade.
