  The prompt emission of gamma-ray bursts (GRBs) is characterized by rapid
variabilities, which may be a direct reflection of the unsteady central engine.
We perform a series of axisymmetric 2.5-dimensional simulations to study the
propagation of relativistic, hydrodynamic, intermittent jets through the
envelope of a GRB progenitor star. A realistic rapidly rotating star is
incorporated as the background of jet propagation, and the star is allowed to
collapse due to the gravity of the central black hole. By modeling the
intermittent jets with constant-luminosity pulses with equal on and off
durations, we investigate how the half-period, $T$, affects the jet dynamics.
For relatively small $T$ values (e.g. 0.2 s), the jet breakout time $t_{\rm
bo}$ depends on the opening angle of the jet, with narrower jets more
penetrating and reaching the surface at shorter times. For $T \leq 1$ s, the
reverse shock crosses each pulse before the jet penetrates through the stellar
envelope. As a result, after the breakout of the first group of pulses at
$t_{\rm bo}$, several subsequent pulses vanish before penetrating the star,
causing a quiescent gap. For larger half-periods ($T=2.0, 4.0$ s), all the
pulses can successfully penetrate through the envelope, since each pulse can
propagate through the star before the reverse shock crosses the shell. Our
results may interpret the existence of a weak precursor in many long GRBs,
given that the GRB central engine injects intermittent pulses with half-period
$T \leq 1$ s. The observational data seem to be consistent with such a
possibility.
