Ask Mr. Smarty Plants

The "Will Fleming" is no doubt a trade name given to the plant by the industry, probably either a selection or cultivar of Ilex vomitoria (yaupon), which is native. Often, a plant that has been bred away from the true form is named after the horticulturist who developed it. Strictly speaking, this puts it out of our range of expertise, as we deal only with plants native not only to North America but to the area in which they are being grown; with cultivars and hybrids we don't necessarily know exactly what is going on. 

From the website Garden Pilot Navigator Ilex vomitoria 'Will Fleming' we extracted this information:

"Distinctly upright form, almost columnar in outline, unfortunately with time will pull apart particularly with ice and snow, a 12' high plant in my trials has splayed and become disoriented, suspect this is a large-growing (15' by 15 to 18') cultivar, male."

All that having been said, we knew from the minute we read your question that the problem is the water on the roots. Yaupon, any yaupon, needs good drainage. It is a good plant for Central Texas, adapted to our often dry, hot climate. Are you sure that amount of 15 inches of irrigation every 3 days is correct? If so, we're surprised everything in your yard isn't dying. That is way too much; perhaps it was just an error in measurements or maybe you meant 15 minutes. However, you probably have alkaline, clay soil, which does not drain well. Whether they can be saved or not, we couldn't say. It's very difficult to add humus, like compost, to soil to improve drainage after the roots are already in the ground. Here are our suggestions: (1) Do whatever you can to direct the water away from the roots of these plants. Our Native Plant Database page on this plant says it will tolerate drought and poor drainage, but it sounds like your bed has NO drainage. (2) Since you say these were recently planted and under windy conditions, they can be treated for transplant shock. Ordinarily, we recommend that woody plants such as yaupon be planted in late Fall or very early Spring, before the heat kicks in and while the plants are partially dormant. Trim off about 1/3 of the upper portions of these plants which, with the reduction of water on the roots, may allow the roots to simply get water up to the top leaves so they can continue to manufacture food for the whole plant. 

If that doesn't work, and the plants do die, we suggest before you put any plant back to replace them, you prepare the beds, perhaps raising the level with lots of compost dug in, don't plant them until Fall, and careful with the water.