Recent work in speech enhancement has proposed a polynomial eigenvalue decomposition (PEVD) method, yielding significant intelligibility and noise-reduction improvements without introducing distortions in the enhanced signal [1]. The method relies on the estimation of a space-time covariance matrix, performed in batch mode such that a sufficiently long portion of the noisy signal is used to derive an accurate estimate. However, in applications where the scene is nonstationary, this approach is unable to adapt to changes in the acoustic scenario. This paper thus proposes a frame-based procedure for the estimation of space-time covariance matrices and investigates its impact on subsequent PEVD speech enhancement. The method is found to yield spatial filters and speech enhancement improvements comparable to the batch method in [1], showing potential for real-time processing.