  We study theoretically a dilute gas of identical fermions interacting via a
p-wave resonance. We show that, depending on the microscopic physics, there are
two distinct regimes of p-wave resonant superfluids, which we term "weak" and
"strong". Although expected naively to form a BCS-BEC superfluid, a
strongly-resonant p-wave superfluid is in fact unstable towards the formation
of a gas of fermionic triplets. We examine this instability and estimate the
lifetime of the p-wave molecules due to the collisional relaxation into
triplets. We discuss consequences for the experimental achievement of p-wave
superfluids in both weakly- and strongly-resonant regimes.
