Experimentally measured parallel ion flows in the standard quasihelically symmetric configuration of the HSX stellarator show a large discrepancy with previous neoclassical calculations, whereas flow in a symmetry degraded configuration is in reasonably good agreement with neoclassical theory. To examine this discrepancy, the neoclassical transport code PENTA has been modified to include collisions with background neutrals. It has been found that the flow damping due to ion-neutral friction significantly modifies the ion parallel flows in the standard configuration. This makes the modeling of the ion parallel flow agree better with the experimental measurements. In the symmetry degraded configuration, higher neoclassical viscosity makes the flow damping arising from neutral friction less important. The bootstrap current was found to be insensitive to the neutral friction as the decrease in ion flow was matched by an increase in the electron flow.