We fabricated stochastic antireflective structures (ARS) and analyzed their stability against high power laser irradiation and high temperature annealing. For 8 ps pulse duration and 1030 nm wavelength we experimentally determined their laser induced damage threshold to 4.9 (±0.3) J/cm(2), which is nearly as high as bulk fused silica with 5.6 (±0.3) J/cm(2). A commercial layer stack reached 2.0 (±0.2) J/cm(2). An annealing process removed adsorbed organics, as shown by XPS measurements, and significantly increased the transmission of the ARS. Because of their monolithic build the ARS endure such high temperature treatments. For more sensitive samples an UV irradiation proved to be capable. It decreased the absorbed light and reinforced the transmission.