Actually, it could also be hormonal, in that the hormone(s) that cause the refractory period do not come into play or aren't present. Check out "male refractory period" on Wikipedia or from other sources. Here is from that article:
"An increased infusion of the hormone oxytocin during ejaculation is believed to be chiefly responsible for the male refractory period, and the amount by which oxytocin is increased may affect the length of each refractory period. Another chemical which is considered to be responsible for the male refractory period is prolactin, which represses dopamine, which is responsible for sexual arousal. Because of this, there is currently an experimental interest in drugs which inhibit prolactin ... Anecdotal reports on cabergoline suggest it may be able to eliminate the refractory period altogether, allowing men to experience multiple ejaculatory orgasms in rapid succession.
...
"Although rarer, some males exhibit no refractory period or a refractory period lasting less than 10 seconds. A scientific study attempting to document natural, fully ejaculatory, multiple orgasms in an adult man was conducted at Rutgers University in 1995. During the study, six fully ejaculatory orgasms were experienced in 36 minutes, with no apparent refractory period. Later, P. Haake et al. reported a single male producing multiple orgasms without elevated prolactin response."
So in any case, it looks like you're not the only one. The Wikipedia article included links, presumably it has one to the Rutgers study, you might look up the article and see if the study gives further enlightenment.
If the hormonal explanation is correct, which sounds smarter than my earlier guess, it doesn't sound like what you've got is a bad thing medically speaking, unless your body needs oxytocin or prolactin for something else and you don't get an increase in those hormones at other times when you need them. (In your shoes I'd be interested in seeing the Rutgers study just to find out if it sheds light on that particular question.)
The reason a penis gets soft after orgasm is kind of like hydraulics. The penis fills with blood that can't get out until there is sexual release, and in most guys after the release the blood can get out and it does leave. In you, obviously it doesn't leave. (Women know this sensation, this is why women can have many orgasms in a row. The blood stays in the genital region until she feels like stopping.)
I would guess (check with a urologist some time to be sure) that probably it's not dangerous, unless the urologist thinks the blood *should* be able to escape from the shaft. It just kind of sounds like your release valve is pretty small, and the blood does not leave.