We present both time-averaged and time-resolved transport measurements of a two-dimensional electron (Wigner) crystal on the surface of superfluid helium confined in a narrow microchannel. We find that the field-current characteristics of the driven crystal obtained by the time-averaged measurements exhibit oscillations and negative differential conductivity. This unusual transport behavior was observed previously by Glasson et al. [Phys. Rev. Lett. 87, 176802 (2001)] and was attributed to a nonequilibrium transition of the electron system to a novel dynamically ordered phase of current filaments aligned along the channels. Contrarily to this explanation, our time-resolved transport measurements reveal that oscillating field-current characteristics appear due to dynamical decoupling (slipping) and recoupling (sticking) of the uniform electron crystal to the liquid helium substrate. Our result demonstrates that this unusual non-linear transport effect is intrinsic, does not depend on the device geometry, and is associated with the dynamical interaction of Wigner crystal with the surface excitations of the liquid substrate.