priapism

A potentially painful or harmful medical condition in which the erect penis does not return to its flaccid state (despite the absence of both physical and psychological stimulation), often as a result of a spinal injury.

An instance of this.

Phosphorus has long been considered a powerful stimulant. It acts upon the generative organism, it is recorded, in a manner to cause the most violent priapisms.

The obsessive focus on one's genitals or on the need for genital gratification.

[M]any on the right have found themselves justifying our current president's priapism with the same arguments that liberals once used to excuse Clinton.