A relationship between deep moonquake occurrence and tidal forcing is suggested by the monthly periodicities observed in the occurrence times of events recorded by the Apollo Passive Seismic Experiment. In addition, the typically large S wave to P wave arrival amplitude ratios observed on deep moonquake seismograms are indicative of shear failure. Tidal stress, induced in the lunar interior by the gravitational influence of the Earth, may influence moonquake activity. We investigate the relationship between tidal stress and deep moonquake occurrence by searching for a linear combination of the normal and shear components of tidal stress that best approximates a constant value when evaluated at the times of moonquakes from 39 different moonquake clusters. We perform a grid search at each cluster location, computing the stresses resolved onto a suite of possible failure planes, to obtain the best fitting fault orientation at each location. We find that while linear combinations of stresses (and in some cases stress rates) can fit moonquake occurrence at many clusters quite well; for other clusters, the fit is not strongly dependent on plane orientation. This suggests that deep moonquakes may occur in response to factors other than, or in addition to, tidal stress. Several of our inferences support the hypothesis that deep moonquakes might be related to transformational faulting, in which shear failure is induced by mineral phase changes at depth. The occurrence of this process would have important implications for the lunar interior.