  We study collisional loss of a quasi-one-dimensional (1D) spin-polarized
Fermi gas near a $p$-wave Feshbach resonance in ultracold $^6$Li atoms. We
measure the location of the $p$-wave resonance in quasi-1D and observe a
confinement-induced shift and broadening. We find that the three-body loss
coefficient $L_3$ as a function of the quasi-1D confinement has little
dependence on confinement strength. We also analyze the atom loss with a
two-step cascade three-body loss model in which weakly bound dimers are formed
prior to their loss arising from atom-dimer collisions. Our data are consistent
with this model. We also find a possible suppression in the rate of dimer
relaxation with strong quasi-1D confinement. We discuss the implications of
these measurements for observing $p$-wave pairing in quasi-1D.
