Well, from the picture, that looks like an Arizona ash tree... one of which we have had in the yards of our last 2 homes.

They are fast growing trees that provide nice shade, but they don't usually last more than 10 to 15 years. Mostly because they are a soft wood, and Texas has a ton of boring insects that love them for chow...

Ours did the same thing by losing leaves right after they bloomed. It is because the boring insects have eaten all of the conduits that transport fluids to the leaves... ergo, they die off quickly and drop to the ground. When you cut the tree up, if you look inside the wood you will probably see the holes where the borers have made their home...

If you want a really good replacement, either get an Oak (which takes so long to grow you will be long gone before you can reap the rewards of its shade) or, better yet, a Texas ash which is fast growing and is specially bred to be borer resistant.

We got one for the front yard and it is great... Growing like gangbusters and it only took 4 years to get big.