The deployment of liquid ammonia as a carbon-neutral fuel for detonation-based propulsion is contingent upon understanding and controlling its complex two-phase combustion dynamics. While the propagation instabilities of gaseous ammonia-hydrogen mixtures have been recently characterized [1, 2], the intrinsic mechanisms governing liquid ammonia detonation—particularly under superheated conditions—remain underexplored. This study elucidates the instability regimes specifically induced by boiling phenomena. A two-phase detonation solver, previously developed and validated by the authors [3], is employed to solve the detonation problem of low-temperature ammonia droplets. We integrate a 32-species, 203-reaction skeletal chemical kinetic mechanism with various phase-change models. Numerical results demonstrate that while conventional evaporation models predict stable propagation, the inclusion of boiling physics triggers a distinct pulsating instability. This regime is characterized by a periodic decoupling of the leading shock from the reaction zone. To provide a mechanistic interpretation, we perform a nonlinear stability analysis derived from shock dynamics theory. The theoretical model identifies bifurcation points governed by the ratio of evaporation to reaction timescales (α). It is revealed that the instability arises from a resonance effect when these two timescales become comparable (α∼O(1)), while stability is observed when the timescales are distinctly separated. These findings offer a fundamental criterion for predicting the stable operation boundaries of ammonia-fueled detonation engines.