Ice sheets experience cyclical forcing that can vary from diurnal to Milankovitch timescales. Observations show seasonal to decadal variations, e.g., in velocity, thickness or ice-front position, due to external forcing such as changes in basal conditions or oceanic circulation. In general, the observed changes can be driven by individual, or combined, variations in external forcings, although it might be hard to identify the contribution of each forcing. We analyze the sensitivity of ice-sheet dynamics by considering perturbations of various parameters that represent the lumped effect of such processes on a seasonal timescale. More specifically, sensitivity to cyclical perturbations around nominal values, of various system parameters, is analyzed by focusing on the response of the grounding-line, the dynamics of which play a key role in the behavior of ice sheets. The cyclical perturbations are applied individually, or in combination, with various phase lags. The results of these experiments are then compared to those found by applying the nominal values constant in time. Using an isothermal heuristic model, it is shown that there may be cases where the asymmetry between the advance and retreat of the grounding-line position may lead to a bias from the steady-state positions corresponding to the nominal values. Even though results are qualitatively similar in both cases, backtilted ("West-Antarctica like") geometry is shown to be more sensitive to cyclical perturbations, compared to downsloping ("Greenland like") geometry.