  The $\Lambda$ hyperon spin flip and non-flip cross sections are calculated in
a simple hadronic model by including both the $s$-channel process involving the
spin 3/2, positive parity $\Sigma^*(1358)$ resonance and the $t$-channel
process via the exchange of a scalar $\sigma$ meson. Because of its large mass,
the $\Lambda$ spin flip to non-flip cross sections is negligibly small in the
$t$-channel process compared to the constant value of 1/3.5 in the $s$-channel
process. With the $s-$channel $\Lambda-\pi$ spin-dependent cross sections
included in a schematic kinetic model, the effects of hadronic scatterings on
the $\Lambda$ spin polarization in Au-Au collisions at $\sqrt{s_{NN}}=7.7$ GeV
are studied. It is found that the $\Lambda$ spin polarization only decreases by
7-12\% during the hadronic stage of these collisions, which justifies the
assumption in theoretical studies that compare the $\Lambda$ polarization
calculated at the chemical freezeout to the measured one at the kinetic
freezeout.
