Stability of slotted ALOHA systems with retransmission cutoff, in which a packet is discarded after the certain number of unsuccessful transmissions, is investigated on slow-frequency-hopped channels with the aid of the catastrophe theory. The result of this paper can be viewed as extension of the result derived by Kim. The balance function is first formulated. Then, the cusp point and the bifurcation sets are numerically evaluated. We visualize how retransmission cutoff effects on bistable region. Using the result, we can design parameters of slotted ALOHA systems with retransmission cutoff such that the system operates with the unique stable equilibrium point.