He stretches out a little, doesn't actually squat. He is not drinking more than he used to. No dogs lived here before and they put in brand new carpet before we moved in. He does not go in the same place every time. This morning it was while coming up the stairs, all the way across the living room and into the bedroom. He does signal that he needs to go out, he stands in front of me and stares at me, when I ask him if he wants to go out, he jumps up and spins around and runs to the door. Then he just stands there outside about 50% of the time. The floor is new carpet. low pile textured. And I clean up with water and shop vac.
There is a product called a belly band that helps with this issue in a male dog. You can see these here:
I would try to give him a better signal to use to get your attention for when he has to urinate or defecate. Put a bell or other noise maker on the door low enough for the dog to reach. Each time you take the dog out, ring the bell. The dog will associate ringing the bell with going out and one day ring the bell to signal to you that he needs to go out. This takes the guess work out of it and if you are busy, you will hear the bell.
If a medical cause is ruled out, you might want to retrain him again. I would do crate training as it prevents them from going on the floors and it also teaches them that they have to go out when you take them outside. You can reward them eliminating outside with tasty treats like hot dog slices or liver slivers. With crate training they also are rewarded with time outside the crate when they eliminate outside. Initially keep that time down to like 30 minutes out of the crate when they eliminate outside. Here is a site on crate training.
You might also feed and water on a set schedule keeping a log of the times he eats and drinks and when he urinates and defecates. Most dogs have a schedule and if you can figure out his schedule, you can plan on having him outside those times he is most likely to have to go.
You might also try leashing him to you so that you can see when he starts to lean forward a bit and then give a little tug and firm NO and take him outside. If he won't eliminate with a leash on, perhaps letting him trail it in the house will be enough to prevent the urination.
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