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We use molecular dynamics (MD) simulation to evaluate the energy loss of a charged projectile moving parallel to a two-dimensional strongly coupled dusty plasma and compare the results with those obtained from the quasilocalized charge approximation (QLCA) and the Vlasov-random phase approximation. Good agreement is found between the QLCA and MD results when the projectile-dust coupling is weak. In the opposite regime, nonlinear effects in the dust-layer response render the QLCA model increasingly inadequate for calculating the energy losses at low projectile speeds.