  We present specific star-formation rates for 40 UV-bright galaxies at
$z\sim7-8$ observed as part of the Reionization Era Bright Emission Line Survey
(REBELS) ALMA large program. The sSFRs are derived using improved measures of
SFR and stellar masses, made possible by measurements of far-infrared (FIR)
continuum emission and [CII]-based spectroscopic redshifts. For each source in
the sample, we derive stellar masses from SED fitting and total SFRs from
calibrations of the UV and FIR emission. The median sSFR is $18_{-5}^{+7}$
Gyr$^{-1}$, significantly larger than literature measurements lacking
constraints in the FIR. The increase in sSFR reflects the larger obscured SFRs
we derive from the dust continuum relative to that implied by the UV+optical
SED. We suggest that such differences may reflect spatial variations in dust
across these luminous galaxies, with the component dominating the FIR distinct
from that dominating the UV. We demonstrate that the inferred stellar masses
(and hence sSFRs) are strongly-dependent on the assumed star formation history
(SFH) in reionization-era galaxies. When large sSFR galaxies are modeled with
non-parametric SFHs, the derived stellar masses can increase by an order of
magnitude relative to constant star formation models, owing to the presence of
a significant old stellar population that is outshined by the recent burst. The
[CII] line widths in the largest sSFR systems are often very broad, suggesting
dynamical masses that are easily able to accommodate the dominant old stellar
population suggested by non-parametric models. Regardless of these systematic
uncertainties in the derived parameters, we find that the sSFR increases
rapidly toward higher redshifts for massive galaxies ($9.6<\log(\rm
M_*/M_{\odot})<9.8$), with a power law that goes as $(1+z)^{1.7\pm0.3}$,
broadly consistent with expectations from the evolving baryon accretion rates.
