Nah, not all males, just some difficult ones :D :D :D :D
I was thinking up the same road as Anne, but I doubt it's an infection. It sounds more behavioral.
But if you think it is an infection, you could give him some cranberry juice or capsules. I know that helped to improve and prevent UTI's in my Yorkie. She really loved chowing down on the capsules, more than drinking the juice :)
Does he piddle right in front of you or is it a kind of behind the back when you're not around to let him out thing? If it's in front of you, it's more likely to be medical. Behind your back, laziness, not clear on communicating needs to you, or just uncaring????
I had to really work hard with Chienne to have her come to me and "tell" me that she needed to go outside, esp. if I was upstairs. I've also given her some homeopathic meds that helped to tighten her muscles. The training and the meds worked well in conjunction.
But we've surrendered to the fact that if she's allowed to roam around the house at night, for some odd reason, she will either piddle or poop. It's as if she doesn't want to bother us

. If she's confined to a room (ours), she'll be happy and dry all night long. So with the A/C on, we shut the door, or we use a baby gate.
I think it might be leftover from her early puppy years when she had access to a doggy door all night long and just never got into a habit of "officially" letting us know her needs.
Good luck Sharon.... I just think of the amount I've cleaned up vs. your small "horse" ;) :d I really feel for you.