A neutered or unneutered male might wet in the house if something has upset him or has an infection.

In one case, it had a social cause. An associate had a well housebroken neutered chihuahua mix. The neighbor's new adopted dog, a Golden Retriever did something... too rough with the little guy (I wasn't there to see). After the chi-mix was brought back into the house, he was visibly upset. The little guy started lifting his leg to mark the doors and furniture in the main traffic areas of the house. The owners were bewildered.

As the "dog person" at work, the head of the household came to my lab to ask me what I thought was going on with their little dog. After I got the story and asked a few other questions, I got the impression the little dog was doing it to be sure that the GR would not violate this territory - he was that upset. I was told he wasn't physically injured but had apparently been terrified. They decided not to amplify the stress and yell at the dog for peeing in the house, but worked with him and avoided interfacing with the overly rough young, adopted GR again. Apparently whatever they did worked as the little dog was soon confident again and didn't mark up his house any more.

In my experience some neuters do have romantic inclinations with certain bitches so they may lift their leg and strut around the house as if they were studs.

In general, any male or female dog, neutered or not, who breaks training in the house generally need to be treated like a puppy and be 'housebroken' again. Here's a link from one of our rescue dog correspondents: Housebreaking the second time around - and quoting from that:
Reasons for house-soiling.
The most common housetraining problem is the male, neutered or intact, who lifts his leg in the house. This is sometimes a display of dominance, though it is also seen in cases where a dog is simply exploring his place in the hierarchy of the household. The next most commonly encountered problem is that of the dog that has never been house-trained in the first place. This dog is often unused to anticipating bodily needs and unaware that he can "ask" for help.
I'm generally involved with very large dogs (flock guardian breeds) but I know small dogs, even neutered males can break training, sometimes for surprising reasons. Dog's just don't think the way we do. It probably depends more on the individual dog and circumstances, than it does with what breed it might be.
Having said all that, I have owned an intact Anatolian male (he was trained to be my service dog) which after his first year, never broke training indoors anywhere. He would also pee on command.