Large eddy simulation (LES) results are presented for a premixed methane/air turbulent flame arising from a confined laboratory-scale single-nozzle burner. The jet issuing from an off-centered nozzle facilitates the development of a large-scale, dominant lateral recirculation zone that stabilizes the flame. A self-sustained jet oscillation is present, which intermittently causes extreme flame fluctuations such as blowout and relight events in the bottom section of the combustion chamber. The combined probability density function transport approach with the Eulerian stochastic fields method is used to numerically investigate the influence of this jet oscillation on combustion stability at the operating condition near lean blowout. The general structure of the flow, including the formation of the recirculation zones depending on the location of the flapping jet, is well-reproduced together with the mean and fluctuating velocity profiles. The behavior of the jet oscillation is investigated using a popular decomposition method known as proper orthogonal decomposition (POD) based on the predicted three-dimensional flow fields. Thanks to POD, the evolution of the simulated flame structure featuring a pronounced flame fluctuation is compared against that experimentally measured according to the phase angles of the low-order modeled jet motion. The absence of the most dominant coherent structure at a single frequency is due to a feedback mechanism between the jet oscillation and combustion process. The simulation shows that a low-frequency jet flapping causes the flame blowout and flashback in the bottom section of the combustor and a stable flame persists as long as the jet flapping rate exceeds a critical value.