There is a misconception that the dog's urine has a high ph balance and that's why it kills grass. In reality, the harmful nutrient that is in dog uring is nitrogen. Sound familiar? It's the very same thing that Scott's puts in it's fertilizer to make your grass green and beautiful. The problem with dog urine is that it has a very concentrated amount of nitrogen in a very small area. As it sinks into the soil, it goes deep, but also wide. As it disperses out, it's concentration is lower and actually impoves your grass. But in the middle, it's too strong and kills it. That's why if you look at teh grass immediately surrounding the dead spot caused by your dog, it is a very lush, dark green.
I inherited a beautiful lawn when I bought my house in 2002. Unfortunately, my female golden retriever was leaving horrible pee burns everywhere. I tried the pills that were supposed to help (they are a ripoff), I tried following her around with a hose and watering where she went, and I tried using a sprinkler to constantly water the entire lawn. Nothing worked, so I went to plan B. I retrained my dog to go in a specific area. It is an area that has small white pebbles. It was quite a battle and caused my dog anxiety. She was soo confused as to why the grass was suddenly "bad". But after a two month battle, she adapted and I haven't had a pee burn in four years.