The response of a dislocation network subject to a periodic external stress is simulated in the kink representation. Kink-kink and kink-pinning point interactions lead to a local, random reduction in the breakaway stress, so that a certain fraction of the total dislocation line is critically pinned according to a self-organized pattern. Mechanical dissipation caused by critically pinned dislocation segments is suggested to be responsible for the finite values of the decrement function measured experimentally at low frequencies.