Numerical simulations based on microscopic approach are used to explore the spin dynamics encountered in the recently reported hyperpolarized (129)Xe NMR maser [D. J. Y. Marion, G. Huber, P. Berthault, and H. Desvaux, ChemPhysChem 9, 1395-1401 (2008)] where series of amplitude modulated rf emissions are observed. The integration of the dynamic features of the electronic detection circuit in the present simulations, based on non-linear Maxwell-Bloch differential equations with dipole-dipole interactions, allows us to prove that the experimentally observed extremely random amplitude modulations crucially require the long-distance dipolar couplings between the nuclear spins with the feedback field acting as an amplifier. The massive dipolar couplings act, when the magnetization is largely tilted off the longitudinal axis, as an apparent transverse self-relaxation mechanism which destroys coherence. This, in particular, explains why the final magnetization after emissions can still be opposite to the magnetic field direction, i.e., being in an unstable state.