Well I'll say it. You are watering too frequently. Because they get a drink every day, your roots do not need to grow any deeper than the top surface of the soil. They stop there because there is no water down deep. Then when there is the slightest change in humidity, the soil surface dries out and the roots dry out. Whereas if you watered deeply, the moisture would penetrate into deeper layers. As the surface of the soil dries out, the roots "realize" there is moisture deeper down and will grow deeper into the soil to tap the reservoir of moisture down there. But from where you are now, you will have to wean the grass off the frequent watering. Start by skipping a day of watering and see if the grass wilts. If not, then water the next day but water for twice as long. Then see how much you can skip before watering again for that same time (30 minutes). Every sprinkler system delivers water at different rates. Getting to 1 inch per week is sort of a goal, but it is also just the starting point. See how your grass grows at that rate. You might be able to go to watering every 10 - 14 days with your relatively cool temps. There are a lot of factors that bear on the situation. I believe you have a disease process going on, so hopefully dropping way back on the frequency of watering will stop that without doing anything else.

I cant say for sure because I don't know how short you cut your grass but keeping it about 3 or 3.5 inches can lessen the chances of it burning. It's also better for your lawn because it needs less watering. This applies only to blue/fescue/rye type lawns as I think Bermuda grass lawns are supposed to be kept short to thrive. Other than that I would keep the hose or a watering can handy and douse the spot asap after she pees to dilute it.

I'll retake pictures soon. That was cut with a brand new ryobi 40v electric mower. Wonder why the blades arent very sharp to begin with?

here are few more photos these are in my backyard. seem like the same plant. 1st one is 7 inches tall and the other 2 photos seems like the same plant but fully matured.