  We present an analysis of a 37-ks observation of the supergiant fast X-ray
transient (SFXT) IGR J17391-3021 (=XTE J1739-302) gathered with Suzaku. The
source evolved from quiescence to a low-activity level culminating in three
weak flares lasting ~3 ks each in which the peak luminosity is only a factor of
5 times that of the pre-flare luminosity. The minimum observed luminosity was
1.3x10^33 erg/s (d/2.7 kpc)^2 in the 0.5--10 keV range. The weak flares are
accompanied by significant changes in the spectral parameters including a
column density (nH = (4.1+-0.5)x10^22 /cm^2) that is ~2--9 times the absorption
measured during quiescence. Accretion of obscuring clumps of stellar wind
material can explain both the small flares and the increase in nH. Placing this
observation in the context of the recent Swift monitoring campaign, we find
that weak-flaring episodes, or at least epochs of enhanced activity just above
the quiescent level but well below the moderately bright or high-luminosity
outbursts, represent more than 60+-5% of all observations in the 0.5--10keV
energy range making this the most common state in the emission behavior of IGR
J17391-3021
