Yes, this happens to me sometimes. Usually when it's been awhile since I had sex (either with myself or someone more exciting ...).
I don't worry about it much, and have sort of assumed it was basically like a wet dream (though not as much fun) -- that is, the body shedding itself of excess semen.
But come to think about it, your question is a good one. I haven't heard much about this, um, phenomenon elsewhere. Anyone else experience this, and/or know where it, um, comes from?
[PS: Arsenal, you might want to consider fixing the typo in your thread headline. "Prostrate juice," while amusing to contemplate (e.g., lying down and being forcibly milked, maybe ....?), really doesn't capture the intent of your question. As I suspect you've realized by now, the correct spelling is "prostate," not "prostrate."]