  We study the stability of p-wave superfluidity against quantum fluctuations
in two-dimensional Fermi gases near a p-wave Feshbach resonance . An analysis
is carried out in the limit when the interchannel coupling is strong. By
investigating the effective potential for the pairing field via the standard
loop expansion, we show that a homogeneous p-wave pairing state becomes
unstable when two-loop quantum fluctuations are taken into account. This is in
contrast to the previously predicted $p + ip$ supefluid in the weak-coupling
limit [V. Gurarie et al., Phys. Rev. Lett. 94, 230403 (2005)]. It implies a
possible onset of instability at certain intermediate interchannel coupling
strength. Alternatively, the instability can also be driven by lowering the
particle density. We also discuss the validity of our analysis.
