Ask Mr. Smarty Plants

Chilopsis linearis (desert willow) is a desert plant, native to this area, and quite accustomed to taking care of itself in terms of water, soil, etc. as you will see from its Growing Conditions below, which mentions avoiding excessive water and fertilizer, and providing good drainage.

"Growing Conditions

Water Use: Low
Light Requirement: Sun
Soil Moisture: Moist , Dry
CaCO3 Tolerance: Medium
Drought Tolerance: High
Cold Tolerant: yes
Heat Tolerant: yes
Soil Description: Well-drained limestone soils preferred, but also does well in sands, loams, clays, caliches, granitic, and rocky soils. Minimal organic content the norm.
Conditions Comments: Allow to dry out between waterings, as this will encourage more extensive waves of blooms. Avoid excessive water and fertilizer, as that can lead to overly rapid growth, fewer blooms, and a weaker plant. Prolonged saturation can result in rot. Won't grow as fast or get as large in clay soil but won't suffer there either. Can be drought-deciduous in some regions. Can survive temperatures as low as 10 degrees F."

What we don't know is how long the tree has been planted, when it was planted, and how the hole was prepared. The symptoms sound very much like transplant shock. If it was planted during the summer months, or has bad drainage so that water is standing on its roots, or has been overfed and overwatered, it simply can't take all that attention. It is used to desert soils, so the addition of organic material to the soil can cause problems for it. 

We are not plant pathologists, and can't say for sure what is wrong with your desert willow, but have the following suggestions, as seen in the Growing Conditions above:

1. Don't water until the soil feels dry.

2. Make sure it is in full sun, which we consider to be 6 or more hours of sun a day.

3. Don't fertilize it; never fertilize a stressed plant.

4. Trim away any branches that appear dead, and remove dead leaves. Discard those cuttings away from the plant, in case the brown spots are something fungal that could be re-transmitted to the plant.  By the same token, keep any fallen leaves or branches raked up and removed.

The plant is drought deciduous, so if it gets too dry, it might start dropping its leaves. It also grows naturally in water courses, ditches and streambeds, which infers deep sources of moisture to the roots. If the drainage around the plant is good, try deep watering, sticking a hose down in the soil and letting it dribble until water appears on the surface, but do this infrequently. 

From the Pima Co. (AZ) Cooperative Extension, we found this article that pretty well summarizes the care of a desert willow.

From our Native Plant Image Gallery:

Chilopsis linearis

Chilopsis linearis

Chilopsis linearis

Chilopsis linearis