Measurements of bright stars passing through the fields of view of the inner coronagraphs (COR1) on board the Solar Terrestrial Relations Observatory (STEREO) are used to monitor changes in the radiometric calibration over the course of the mission. Annual decline rates are found to be 0.648 +/- 0.066%/year for COR1-A on STEREO Ahead and 0.258 +/- 0.060%/year for COR1-B on STEREO Behind. These rates are consistent with decline rates found for other space-based coronagraphs in similar radiation environments. The theorized cause for the decline in sensitivity is darkening of the lenses and other optical elements due to exposure to high-energy solar particles and photons, although other causes are also possible. The total decline in the COR-B sensitivity when contact with Behind was lost on 1 October 2014 was 1.7%, while COR1-A was down by 4.4%. As of 1 November 2017, the COR1-A decline is estimated to be 6.4%. The SECCHI calibration routines will be updated to take these COR1 decline rates into account.