  We investigate the pulsational stability of massive (M >~ 120 Msun) main
sequence stars of a range of metallicities, including primordial, Population
III stars. We include a formulation of convective damping motivated by
numerical simulations of the interaction between convection and periodic shear
flows. We find that convective viscosity is likely strong enough to stabilize
radial pulsations whenever nuclear-burning (the epsilon-mechanism) is the
dominant source of driving. This suggests that massive main sequence stars with
Z <~ 2 x 10^-3 are pulsationally stable and are unlikely to experience
pulsation-driven mass loss on the main sequence. These conclusions are,
however, sensitive to the form of the convective viscosity and highlight the
need for further high-resolution simulations of the convection-oscillation
interaction. For more metal-rich stars (Z >~ 2 x 10^-3), the dominant
pulsational driving arises due to the kappa-mechanism arising from the
iron-bump in opacity and is strong enough to overcome convective damping. Our
results highlight that even for oscillations with periods a few orders of
magnitude shorter than the outer convective turnover time, the "frozen-in"
approximation for the convection-oscillation interaction is inappropriate, and
convective damping should be taken into account when assessing mode stability.
