A model of a long optical communication line consisting of alternating segments with anomalous and normal dispersion, whose lengths are picked randomly from a certain interval, is considered. As the first stage of the analysis, we calculate small changes in parameters of a quasi-Gaussian pulse passing a double-segment cell by means of the variational approximation (VA) and we approximate the evolution of the pulse passing many cells by smoothed ordinary differential equations with random coefficients, which are solved numerically. Next we perform systematic direct simulations of the model. Simulations reveal slow long-scale dynamics of the pulse, frequently in the form of long-period oscillations of its width. It is thus found that the soliton is most stable in the case of zero path-average dispersion (PAD), less stable in the case of anomalous PAD, and least stable in the case of normal PAD. The soliton's stability also strongly depends on its energy, the soliton with low energy being much more robust than its high energy counterpart.