Iron losses strongly influence ferroresonance behavior of power transformers. While a jump-up is the characteristic of the non-linear magnetizing branch, the jump-down phenomenon can only be described when losses or loads are considered. In this article, the impact of core losses (constant resistance or non-linear resistancce) on the turning points of the bifurcation diagram of a ferroresonance circuit is investigated by a developed 2-D bifurcation diagram. The sensitivity of solutions with respect to the circuit parameters are analyzed and discussed. It is shown that the left-side turning point is more affected by the non-linear core loss model than the right side is. Based on the developed method, an operational guideline for the range of values of the load that avoids the jump between steady-state solutions and ferroresonance overvoltages with different source voltage amplitudes is provided. The results obtained by analytical approach are compared with time domain simulations.