Blowdown monopropellant propulsion systems are favored in space missions for their simplicity and reliability but are prone to chugging instability, a low-frequency combustion instability that can compromise mission success. This study investigates the impact of catalytic reactor design parameters and operating conditions on the stability of such systems through parametric studies using reduced-order models. Parameters including aspect ratio, catalyst size, post-reactor chamber volume, propellant concentration, and catalyst reactivity were analyzed. Results indicate that smaller aspect ratios and catalyst sizes, larger post-reactor chamber volumes, and higher catalyst reactivity enhance stability by optimizing time lags and gas residence times. Conversely, higher propellant concentrations increase instability risks. These findings and the use of reduced-order models in the stability assessment provide essential guidelines for designing stable blowdown monopropellant systems, contributing to more reliable and efficient space propulsion technologies. The use of reduced-order modeling enables fast and cost-effective stability assessment, offering a practical alternative to CFD or hot-fire testing for early-stage design evaluations.