We study the stability of
p-wave superfluidity for two-dimensional Fermi gases near a
p-wave Feshbach resonance. A systematic analysis is carried out in the limit when the interchannel coupling is strong. We show that a homogeneous
p-wave pairing is actually unstable due to quantum fluctuations, in contrast to the previously predicted
p+ip superfluid in the weak-coupling limit [V. Gurarie et al., Phys. Rev. Lett. 94, 230403 (2005)]. This indicates an onset of instability at certain intermediate interchannel coupling strength. Alternatively, the instability can also be driven by lowering the particle density.