That other response also noted that mature trees don't usually need extra landscaping water. It sounds like you have have been overwatering this tree a lot, and the girdling problem might not have come to light if the watering issue hadn't made the tree look bad.
Do try measuring, or research what the rules of thumb are for your type of watering system. Several hours for a typical urban yard sounds excessive. An hour is a lot, and don't some of those landscape watering systems only go 20-30 minutes a zone?
One of the sites I came across yesterday that I didn't link talked about says
http://www.onlinegardener.com/trees/Live%20Oak,%20Texas.pdf:
Quote:
Like most trees, live oak thrives on moist well-drained soils. However, this species tolerates urban conditions including compacted or severely disturbed soils. Live oak tolerates drought conditions and root problems that lead to moisture stress. It is also tolerant of salt spray, which makes it an exceptional species for coastal plantings. Live oak is intolerant of excessive soil moisture due to poor drainage and excessive irrigation. Phytophthora root rot is prevalent in wet soils especially when live oak is growing in heavily irrigated lawns.
You can see that you've set up conditions opposite of what this tree thrives on.