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The dynamics of barrier microdischarges operating in a Townsend regime is studied analytically and via kinetic particle-in-cell/Monte Carlo simulations. It is shown that statistical fluctuations of the number of charged particles in the discharge gap strongly influence the dynamics of natural oscillations of the discharge current and may even lead to a disruption of the discharge. Analysis of the statistical effects based on a simple model is suggested. The role of external sources in stabilizing microdischarges is clarified.