  GRB080503 was classified as a short GRB with extended emission (Perley et al.
2009). The origin of such extended emission (found in about a quarter of Swift
short GRBs) is still unclear and may provide some clues to the identity of the
elusive progenitors of short GRBs. The extended emission from GRB 080503 is
followed by a rapid decay phase (RDP) that is detected over an unusually large
dynamical range (one decade in time and ~3.5 decades in flux). We model the
broad envelope of extended emission and the subsequent RDP using a physical
model (Genet & Granot 2009), in which the prompt emission (and its tail) is the
sum of its individual pulses (and their tails). For GRB 080503, a single pulse
fit is found to be unacceptable. The RDP displays very strong spectral
evolution and shows some evidence for the presence of two spectral components
with different temporal behaviour, likely arising from distinct physical
regions. A two pulse fit provides a much better fit to the data. The shallow
gamma-ray and steep hard X-ray decays are hard to account for simultaneously,
and require the second pulse to deviate from the simplest version of the model
we use. Therefore, while high latitude emission is a viable explanation for the
RDP in GRB080503, it is quite plausible that another mechanism is at work here.
Finally, we note that the properties of the RDP following the extended emission
of short GRBs appear to have different properties than that following the
prompt emission of long GRBs. However, a larger sample of short GRBs with
extended emission is required before any strong conclusion can be drawn.
