First of all, as already said, please take him to the vet, and rule out problems. UTI is the first thing that comes to mind, but there could be other things, like bladder stones, and others. Don't assume there is nothing physical.

If it is determined that this is behavioral rather than medical, It sounds like you need to go back to housetraining 101. You need to go outside with him, and make sure he urinates several times (males need to go several times, not just once, especially if they are marking), and is truly empty. Many dogs get distracted, and even though they "know what to do out there," they start sniffing or whatever, and forget. You need to be there to remind him to go potty.

It helps to have a key word (I tell my dogs to "Go potty!"), so they know what you mean. To train this, you'll need to wait until he's in the act of urinating, then give your command of choice, and immediately praise him. He'll get it. Then, when he goes outside, and forgets what to do, you can remind him.

And just because he's neutered does not mean he does not want to mark. Based on the fact that you said he's been doing this since you moved into a new house, I'd be inclined to believe this is marking. If he's 2, he's also reaching sexual maturity, so he'll be more wont to mark, too. Many, many spayed and neutered dogs want to mark; it's instinctual, even when the gonads are removed. When cleaning the messes, make sure you clean thoroughly with an enzymatic cleaner that destroys the odor. If the dog can still smell it, he will want to re-mark it. Nature's Miracle is a good cleaner, but not cheap. I like Capture, which I find at Sear's. It's a lot less expensive, and works better, IMHO.

If this problem is not medical (and remember, only a vet can determine that), you may want to confine him when you cannot supervise. And when you can supervise, either tether him to you with a leash, or baby-gate him in the room with you, That way you can see what his signals are, and as soon as he appears to be uncomfortable, or is sniffing or pawing, out the door he goes.