Ask Mr. Smarty Plants

Mr. Smarty Plants thinks that the damage is being caused by insects—probably wood borers or girdlers.  An article from SFGate describes several pests of Prosopis glandulosa (Honey mesquite) including borers and twig girdlers.  In the Cochise County (Arizona) Master Gardener Newsletter, August 2006, Mesquite Trees Under Stress describes several borer insects that could cause the damage you are seeing.  Control of one of these borers, Chrysobothris femorata (Flatheaded appletree borer) is the subject of an article, Managing the Flatheaded Appletree Borer, by Texas A&M AgriLIFE EXTENSION Service.  They describe symptoms of the damage to the tree. The eventual result is the bark splitting away and the limb dying.  You can read about treatment for these borers in an article from SFGate, How to Treat Mesquite for Borers.  University of California IPM Online describes another possible pest of honey mesquites, Roundheaded (Longhorned) Borers, their symptoms and control.  I consulted Dr. Mark Simmons, Director of Research and Consulting for the Ecosystem Design Group at the Lady Bird Johnson Wildflower system who did his dissertation research with honey mesquite.   He says it could be one of the twig girdlers, Oncideres rhodosticta (Mesquite girdler), Oncideres pustulatus (Huisache girdler) or Oncideres cingulata (Pecan girdler).  If so, then you should be able to see the ring where they have eaten the cambium on your tree's branches.  Here are more photos of the mesquite girdler, huisache girdler and pecan girdler from BugGuide.  You could contact your Burnet County AgriLIFE Extension Agent for verification of the pest and recommendations for its control.