Falls are the leading cause of injury related hospitalization and mortality among older adults. Consequently, mitigating age-related declines in gait stability and reducing fall risk during walking is a critical goal for assistive devices. Lower-limb exoskeletons have the potential to support users in maintaining stability during walking. However, most exoskeleton controllers are optimized to reduce the energetic cost of walking rather than to improve stability. While some studies report stability benefits with assistance, the effects of specific parameters, such as assistance magnitude and duration, remain unexplored. To address this gap, we systematically modulated the magnitude and duration of torque provided by a bilateral hip exoskeleton during slip perturbations in eight healthy adults, quantifying stability using whole-body angular momentum (WBAM). WBAM responses were governed by a significant interaction between assistance magnitude and duration, with duration determining whether exoskeleton assistance was stabilizing or destabilizing relative to not wearing the exoskeleton device. Compared to an existing energy-optimized controller, experimentally identified stability-optimal parameters reduced WBAM range by 25.7% on average. Notably, substantial inter-subject variability was observed in the parameter combinations that minimized WBAM during perturbations. We found that optimizing exoskeleton assistance for energetic outcomes alone is insufficient for improving reactive stability during gait perturbations. Stability-focused exoskeleton control should prioritize temporal assistance parameters and include user-specific personalization. This study represents an important step toward personalized, stability-focused exoskeleton control, with direct implications for improving stability and reducing fall risk in older adults.