Scheduled for launch in 2014, Astro-H is the sixth Japanese X-ray astronomy satellite mission. More than 60 silicon avalanche photodiodes (Si-APDs; hereafter APDs) will be used to read out BGO scintillators, which are implemented to generate a veto signal to reduce background contamination for the hard X-ray imager (HXI) and a soft gamma-ray detector (SGD). To date, however, APDs have rarely been used in space experiments. Moreover, strict environmental tests are necessary to guarantee APD performance for missions expected to extend beyond five years. The radiation hardness of APDs, as for most semiconductors, is particularly crucial, since radiation in the space environment is severe. In this paper, we present the results of radiation tests conducted on reverse-type APDs (provided by Hamamatsu Photonics) irradiated by gamma rays ( 60 Co) and 150 MeV protons. We show that, even under the same 100 Gy dose, high energy protons can cause displacement (bulk) damage in the depletion region and possibly change the activation energy, whereas gamma-ray irradiation is less prone to cause damage, because ionization damage dominates only the surface region. We also present quantitative guidance on how to estimate APD noise deterioration over a range of temperatures and radiation doses. As a practical example, we discuss the expected degradation of the BGO energy threshold for the generation of veto signals, following several years of Astro-H operation in Low Earth Orbit (LEO), and directly compare it to experimental results obtained using a small BGO crystal.