  It is well known that particles can get trapped by randomly placed obstacles
when they are pushed too much. We present a model where the current in a
disordered medium dies at a large external field, but is reborn when the
activity is increased. By activity we mean the time-variation of the external
driving at a constant time-averaged field. A different interpretation of the
resurgence of the current is that the particles are capable of taking an
infinite sequence of potential barriers via a mechanism similar to stochastic
resonance. We add a discussion regarding the role of "shaking" in processes of
relaxation.
