A trajectory following the repelling branch of an equilibrium or a periodic orbit is called a canards solution. Using a continuation method, we find a new type of canards bursting which manifests itself in an alteation between the oscillation phase following attracting the limit cycle branch and resting phase following a repelling fixed point branch in a reduced leech neuron model. Via periodic-chaotic alteating of infinite times, the number of windings within a canards bursting can approach infinity at a Gavrilov-Shilnikov homoclinic tangency bifurcation of a simple saddle limit cycle.