An ion-specific electrolyte perturbed-chain statistical associating fluid theory (ePC-SAFT) has been developed to describe the thermodynamic and transport properties of ionic liquids (ILs) for developing IL-based technologies to separate CO2 from gas mixtures. However, as it has been pointed out previously, SAFT-based models can lead to a pitfall, manifesting as an additional fictitious liquid-liquid critical line connected to an additional mechanically stable critical point when modeling pure substances. In this work, a method for detecting a pitfall in ILs was developed, where an expression with ionic term for calculating the critical point with ePC-SAFT was derived and an algorithm for detecting the additional fictitious phase equilibrium for ILs was proposed. The pitfall occurrence for an extended set ILs taken from our previous work was investigated. It shows that a pitfall occurs only for one single IL among all 96 ILs in the temperature and pressure range of interest. For [C(8)mpy][BF4], at 290.27-291.78 K, a pitfall may occur at the pressures of interest; at 273.15-290.20 K, it may occur at any given pressure. The ion-specific ePC-SAFT parameters for [C(8)mpy](+) may therefore need to be modified in the future when more reliable experimental results are available for parameter fitting.