Priapism.

Priapism is a potentially harmful and painful medical condition in which the erect penis or clitoris does not return to its flaccid state, despite the absence of both physical and psychological stimulation, within four hours. There are two types of priapism: low-flow and high-flow. Low-flow involves the blood not adequately returning to the body from the organ. High-flow involves a short-circuit of the vascular system partway along the organ. Treatment is different for each type. Priapism is considered a medical emergency, which should receive proper treatment by a qualified medical practitioner. Early treatment can be beneficial for a functional recovery.

Awesome bonus from Wikipedia: The name comes from the Greek god Priapus (Ancient Greek: Πρίαπος), who was noted for his disproportionately large and permanent erection.

Basically, if it doesn't go down after four hours, they'll have to either drain your penis of it's blood, or cut it off (obviously not for every case, but still, traumatizing none-the-less.)

There have been few AMAs by reddit users that have suffered from it, but this one in particular stuck out in my mind. Poor guy lost his penis to it.

I'm pretty sure if I had to gamble between getting a hardon and losing my dick, I'd be faced with the toughest decision I would have to make in my entire life.