Solutions are developed for the harmonic interior pressurization of idealized hemispherical lava domes to determine the evolution of instability with time. Integrated gas pressure distributions are evaluated to determine uplift on inclined planes of potential detachment that traverse the dome, and to evaluate the limit-equilibrium stability of blocks isolated by these planes. Average pressure distributions show an initial transient rise to peak dynamic gas pressures that corresponds to a harmonic steady state. Progress towards potential instability mirrors this rise, and oscillates with the harmonic steady state. The timing of pressurization of the dome lavas is modulated by a diffusive time. The magnitude of this pressurization is modulated by dome geometry and the magnitude and non-dimensional frequency of the interior inflation. Two distinct pressurization behaviours are apparent: the first, at high relative inflation frequencies, is where the dynamic steady state corresponds to static pressurization at the mean interior pressure; and the second, at low relative inflation frequencies, is where the dynamic state synchronously responds to the oscillating interior-pressure boundary condition, and peak uplift is proportional to the mean pressure plus the maximum harmonic overpressure. These two conditions are separated by a frequency shift, or change in fluid diffusivity, of only two orders of magnitude, and are significant because the destabilizing uplift force may increase by a factor of two, where all other parameters, except excitation frequency or diffusivity, remain fixed. These results are applied to stability evaluations of the lava dome at the Soufriere Hills volcano, to examine failure mechanisms potentially consistent with the observed delay in collapse. Linear models incorporating time-invariant strength and transport parameters are only able to represent collapse for interior gas pressures at the upper limit of observed magnitudes. Conversely, behaviours incorporating fatigue-weakening, or hysteretic permeability enhancement, of the dome rocks are able to approach failure for modest pressurization magnitudes, to match observed delays in collapse and potentially to explain why some domes collapse explosively whereas others do not.