Thanks for the additional information. It is helpful. The first thing you have to do is ensure that you are cleaning the spot well enough to remove the odor. Most cleaners are designed to fool the human nose. A dog's nose is much better at scent detection. You have to break down the protein that cause the odor in order to remove it well enough to fool the dogs nose. Enzymatic cleansers do break down the protein and thus eliminate the odor. Urine also tends to move through carpet, padding and then pool outward when it hits the subflooring. As a result you need to let any cleanser soak in as long as the urine did so it can move through the carpet and padding in the same manner to reach all the urine.
He is not unusual in not wanting to go out in the rain especially if there is a spot inside that smells like an acceptable place to eliminate. In fact they even make a little tent called a poop tent for dogs (mostly small ones) who do not want to eliminate outdoors in the rain, cold or snow. You can see it here:
You can even use a regular small tent and remove the flooring. Once a dog realizes that they don't have to go into the rain, cold or snow, they will be more inclined to go outside. Another options would be to put a sod patch inside. This is something I developed for apartment dwellers but works well for other cases as well.
You take a large pan like a kitty litter pan or even a baby swimming pool. You create a platform frame with wire on top. Place newspaper or other absorbent material such as wood shavings under the platform and place sod on top of the wire frame. Since it is grass, your dog will go on it. You can remove solids and can spray the urine so it moves through and down into the absorbent material underneath. This lets you use the same piece of sod for a while before needing to replace it. You do need to replace the material under the platform.
You do want to keep an eye on him for other symptoms like getting caught behind doors or sofas, or not recognizing people he should know. Breaking house training is a symptoms as well of a condition similar to Alzheimer in humans called Cognitive Dysfunction Syndrome (CDS). It can cause the above symptoms and your dog is elderly. The good news is that there is a drug called L-Selegeline (Anipryl (R)) which has been recently approved for use in the clinical indication of cognitive dysfunction (CDS) in dogs. Sol if he does exhibit these signs in the future, there is a treatment method. Please see this site for more information and other causes that may exhibit the same symptoms.
There really isn't any way of forcing a dog to go out when they don't want to due to weather conditions. If you get a larger tent, you might take him out on the leash into the tent and give him the time necessary to eliminate inside before coming back inside. It will be easier since no one will be getting wet or cold.
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