Well, there is a medical condition called Priapism, where the erection does not subside. It's a medical emergency which without treatment can result in ischemia, thrombosis, impotence, or - in extreme cases - gangrene, resulting in amputation.

The condition is named for the minor Greek god Priapus, who most commonly is depicted with an absurdly large and permanent erection. Apparently some scholars think that garden gnomes are a descendant of Priapus, of sorts....