The high angular resolution technique of non-redundant masking (NRM) or aperture masking interferometry (AMI) has yielded images of faint protoplanetary companions of nearby stars from the ground. AMI on James Webb Space Telescope (JWST)'s Near Infrared Imager and Slitless Spectrograph (NIRISS) has a lower thermal background than ground-based facilities and does not suffer from atmospheric instability. In this paper we quantify factors that limit the raw point source contrast of JWST NRM. We develop an analytic model of the NRM point spread function which includes different optical path delays between mask holes and fit the model parameters with image plane data. In the presence of small piston errors, the dominant sources of closure phase error are flat field errors and unmodeled variations in intra-pixel sensitivity. The in-flight stability of NIRISS will determine how well these errors can be calibrated by observing a point source. Our results help develop efficient observing strategies for space-based NRM.