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This paper investigates the behavior of the spectral resonator-based spectral observer (RBO) for lossy measurements. The RBO is an efficient real-time method designed for measuring the harmonic components of periodic signals. Recently, some experiments have shown that RBO can tolerate some data loss, but no exact criteria of the convergence have been available. The main contribution of this paper is a set of conditions which enable to predict whether the observer is able to find the harmonic components or not. The necessary condition of convergence helps to recognize the situations when the error-free estimation of the harmonic components is not possible. The sufficient conditions of convergence give safe regions of data loss parameters (e.g., data loss ratio) where the unbiased harmonic estimation can always be ensured. Simulations are also presented to demonstrate the effect of data loss in different situations.