This article deals with the recursive filtering issue for an array of two-dimensional systems with random sensor failures and dynamic quantizations. The phenomenon of sensor failure is introduced whose occurrence is governed by a random variable with known statistical properties. In view of the data transmission over networks of constrained bandwidths, a dynamic quantizer is adopted to compress the raw measurements into the quantized ones. The main objective of this article is to design a recursive filter so that a locally minimal upper bound is ensured on the filtering error variance. To facilitate the filter design, states of the dynamic quantizer and the target plant are integrated into an augmented system, based on which an upper bound is first derived on the filtering error variance and subsequently minimized at each step. The expected filter gain is parameterized by solving some coupled difference equations. Moreover, the monotonicity of the resulting minimum upper bound with regard to the quantization level is discussed and the boundedness analysis is further investigated. Finally, effectiveness of the developed filtering strategy is verified via a simulation example.