The narrow rings of Uranus and Neptune exist in a system of observed and hypothesized small moons. Catastrophic fragmentation of these moons by comet impact has been proposed as the mode of origin of those rings, and earlier efforts to model the process showed that small moons are destroyed by impact on short timescales, leading to rapid collisional erosion of any primordial satellite system (Colwell and Esposito, 1992). We reexamine the question of impact fragmentation of small satellites in the light of new observational data on the population of Kuiper Belt and Centaur objects that produce the impacting flux and new theoretical and computational studies of catastrophic fragmentation. We find that the impacting flux used by Colwell and Esposito (1992) is consistent with the new observations of Kuiper Belt objects and calculations of their transport into the solar system. However, new fragmentation criteria from modeling of the asteroid belt and hydrocode simulations lengthen the model collisional lifetimes of satellite systems. The observed distribution of rings, dust bands, and moons at Uranus and Neptune suggest a catastrophic disruption model with a relatively weak dependence on target radius.