Transmission of solitary pulses in a fiber-optic link consisting of alternating dispersive and nonlinear segments (split-step model, or SSM) with uniform loss and lumped gain is studied. By means of systematic simulations, it is found that solitary pulses are stable in this model if it includes, together with the loss and gain, synchronous intensity modulators (SIMs). In particular, it is found that the pulse is stable in a finite interval Lmin < L < Lmax of values of the system's cell-size L. The instability of the pulses in the case L < Lmin, including the limit L → 0, implies that SIMs cannot stabilize pulses in the usual uniform fiber link, which is also shown analytically, while SSM makes the stabilization possible. Stability limits, Wmin and Wmax, are also found in terms of the temporal width W of the SIM transmission window. In addition, a maximum value αmax of the fiber-loss constant α, which admits the existence of stable pulses, is found as a function of gain. If α is close to αmax, then roughly 2/3 of the gain is spent to balance the fiber loss, and the remaining 1/3 is absorbed by SIM-induced loss. The system also provides for suppression of the pulse's temporal jitter induced by random perturbations, and of interaction between pulses.