Microgrids (MGs) are characterised by reduced inertia that can lead to large transients after an islanding event. These transients can result in cascaded device disconnections triggered by protections and consequently to major loss of load or MG blackout. In this paper, a MG operational planning model for grid-connected operation, enhanced with fault-triggered islanding conditions that ensure the MG survivability (both steady-state and dynamic) after islanding is proposed. The dynamic frequency behaviour during islanding using a nonlinear frequency response model is considered by including associated constraints in the planning problem. These include industry limits on the maximum rate of change of frequency, frequency nadir, and the steady-state frequency deviation. The problem is formulated with an iterative multi-stage mixed integer linear model that ensures reliable frequency response, self-sufficiency, and optimal operation of the MG. Simulation results on the CIGRE low-voltage distribution network demonstrate the effectiveness of the proposed model and its suitability in ensuring the reliability, survivability and resilience of a MG.