The soft x-ray spectrometer (SXS) instrument that flew on the Astro-H observatory was designed to perform imaging and spectroscopy of x-rays in the energy range of 0.2 to 13 keV with a resolution requirement of 7 eV or better. This was accomplished using a 6 × 6 array of x-ray microcalorimeters cooled to an operating temperature of 50 mK by an adiabatic demagnetization refrigerator (ADR). The ADR consisted of three stages to operate using either a 1.2 K superfluid helium bath or a 4.5 K Joule-Thomson (JT) cryocooler as its heat sink. The design was based on the following operating strategy. After launch, while liquid helium was present (cryogen mode), two of the ADR's stages would be used to single-shot cool the detectors, using the helium as a heat sink. When the helium was eventually depleted (cryogen-free mode), all three ADR stages would be used to continuously cool the helium tank to about 1.5 K and to single-shot cool the detectors (to 50 mK), using the JT cryocooler as a heat sink. The Astro-H observatory, renamed Hitomi after its successful launch in February 2016, carried ∼36 L of helium into orbit. Based on measurements during ground testing, the average heat load on the helium was projected to be 0.66 mW, giving a lifetime of more than 4 years. On day 5, the helium had cooled to <1.4 K and ADR operation began, successfully cooling the detector array to 50 mK. The ADR's hold time steadily increased to 48 h as the helium cooled to a temperature of 1.12 K. As the commissioning phase progressed, the ADR was recycled (requiring ∼45 min) periodically, either in preparation for science observations or whenever the 50 mK stage approached the end of its hold time. In total, 18 cycles were completed by the time an attitude control anomaly led to an unrecoverable failure of the satellite on day 38. This paper presents the design, operation, and on-orbit performance of the ADR in cryogen mode as the foreshortened mission did not provide an opportunity to test cryogen-free mode.