  A promising formation channel of SMBHs at redshift 6 is the so-called DC
model, which posits that a massive seed BH forms through gravitational collapse
of a $\sim 10^5~M_\odot$ SMS. We study the evolution of such a SMS growing by
rapid mass accretion. In particular, we examine the impact of time-dependent
mass accretion of repeating burst and quiescent phases that are expected to
occur with a self-gravitating circumstellar disk. We show that the stellar
evolution with such episodic accretion differs qualitatively from that expected
with a constant accretion rate, even if the mean accretion rate is the same.
Unlike the case of constant mass accretion, whereby the star expands roughly
following $R_* \simeq 2.6 \times 10^3 R_\odot (M_*/100~M_\odot)^{1/2}$, the
protostar can substantially contract during the quiescent phases between
accretion bursts. The stellar effective temperature and ionizing photon
emissivity increase accordingly as the star contracts, which can cause strong
ionizing feedback and halt the mass accretion onto the star. With a fixed
duration of the quiescent phase $\Delta t_{\rm q}$, such contraction occurs in
early evolutionary phases, i.e. for $M_* \lesssim 10^3~M_\odot$ with $\Delta
t_{\rm q} \simeq 10^3$ yr. For later epochs and larger masses but the same
$\Delta t_{\rm q}$, contraction is negligible even during quiescent phases.
With larger quiescent times $\Delta t_{\rm q}$, however, the star continues to
contract during quiescent phases even for the higher stellar masses. We show
that such behavior is well understood by comparing the interval time and the
thermal relaxation time for a bloated surface layer. We conclude that the UV
radiative feedback becomes effective if the quiescent phase associated by the
burst accretion is longer than $\sim 10^3$ yr, which is possible in an
accretion disk forming in the direct collapse model.
