The long-term dynamics of the internal kink mode are studied using the non-linear, two-fluid magnetohydrodynamics (MHD) code XTOR-2F (Lütjens et al 2010 J. Comput. Phys.229 8130). The dynamics of the internal kink are studied in resistive MHD plus transport, and, in addition, also including some two-fluid effects. The simulation results yield a pattern of kink cycles or stationary states with m/n = 1/1 helicity. The threshold for sustained (non-decaying) kink cycles, which characterize sawtooth oscillations, is shown to depend on the plasma pressure, the current and energy diffusion times, and the ion and electron diamagnetic drifts. In particular, the diamagnetic flow stabilization extends the cyclic kink regime into a parameter space that is adequate to carry out studies of sawtooth oscillations in ohmic tokamak discharges.