This paper presents a technique to increase the stability of a reverberation enhancement system (RES) via time-variation. RESs are installed in rooms to extend the physical reverberation time via electroacoustic feedback. By introducing variations in the feedback path, the probability that energy builds-up is reduced, and therefore the gain before instability is increased. Time-varying mixing of the feedback paths by unitary matrices is guaranteed to be energy-conserving and introduces variations of the added reverberation generated by a feedback delay network. The theory of time-varying matrices is reviewed and a practical demonstration is given.