Priapus. But you probably didn't need us to tell you that.
This is considered one of those "good problems" in a culture where erectile dysfunction ranks a notch above "terror attack" on most men's Panic Scale. This is why the "herbal Viagra" industry dominates email spam. Millions of men think having their groin turned into a pube enshrouded temple of awesome for hours at a time would accomplish most of their life goals.
Why it Would Suck:
The problem with priapism is that nothing can bring your little soldier down from attention. Even when you've had your fun, he's still saluting. Doesn't sound so bad except that, when you're hard all the time it's the result of blood pumping in to the wang but not out. This can lead to blood clots, gangrene and the future inability to ever have an erection again. Oh, and pain. Severe pain.
For people who have to get medical attention for this--and it's not uncommon--the solution starts with the cringe worthy tactic of packing your crotch with ice. If exposure to frostbite inflicting levels of cold fails to work, they can try needles, shunts, drainage and injections of decongestants into your shiny new dicksicle.
Generally speaking, those are the frontline treatments, like say if your wang has been up for more than four hours or so. Some people--like a Peruvian farmer whose name was not provided so we'll just call him Chubs McWeiner--will hold out for eight solid days before seeking medical attention. Eight days with what we have to assume by the end looked an awful lot like a bratwurst stuffed with grape jelly.
In cases like that, surgery is the only option. We won't give you the details of the surgery (we're sure you can find pics of it out there) but let's face it, there's no non-invasive method for surgically deflating your junk.