A lot of times this happens with the weather change. Mine have not changed yet but they are old and well established.
I am a gardening newbie- any other answers? LOL

Just to make sure there isn't something else going on with your tree you might check the watering.

This time of year Mesquite trees only need to be watered once every three to four weeks. The water should soak into the soil at least three feet and should be applied at the drip line (edge of branches) and not next to the trunk. In December and January your tree will only need water once a month and if we get good rains you can probably skip a watering or two.

It also may depend on where you are in AZ. I bet it's the water schedule though.

I've lived here for 10 years, never water my mesquites.
They loose there leaves in the winter but come back
beautiful every spring....

Gemfire