As Don approached the coast it encountered dry air aloft near 95W (its still there). Although Don was a small system, the outer circulation of Don probably had been drawing this dry airmass down from east Texas for quite a few hours as the tropical storm moved closer to the coast. The high temperatures in Laredo were 106 on the 27th, 105 on the 28th and 102 on the 29th with dewpoints in the high 50s to mid 60s. Picking College Station as an example further to the north where the dry air would have originated, the high temperatures for those same days were 103,102 and 99. With northerly winds aloft that were enhanced by the circulation of the storm, the dry air over east Texas (surface and aloft) wiped out the convection before the cyclone reached land in south Texas. Normally in east Texas the summers, under southerly flow, are hot and humid. This year the southerly flow is there at the surface, but its been dry aloft.

Rainfall totals from Don:
Corpus Christi 0.02
Harlingen 0.20
Brownsville 0.63
ED