Traditional joint source-channel coding employs static learned semantic representations that cannot dynamically adapt to evolving source distributions. Shared semantic memories between transmitter and receiver can potentially enable bandwidth savings by reusing previously transmitted concepts as context to reconstruct data, but require effective mechanisms to determine when current content is similar enough to stored patterns. However, existing hard quantization approaches based on variational autoencoders are limited by frequent memory updates even under small changes in data dynamics, which leads to inefficient usage of bandwidth.To address this challenge, in this paper, a memory-augmented semantic communication framework is proposed where both transmitter and receiver maintain a shared memory of semantic concepts using modern Hopfield networks (MHNs). The proposed framework employs soft attention-based retrieval that smoothly adjusts stored semantic prototype weights as data evolves that enables stable matching decisions under gradual data dynamics. A joint optimization of encoder, decoder, and memory retrieval mechanism is performed with the objective of maximizing a reasoning capacity metric that quantifies semantic efficiency as the product of memory reuse rate and compression ratio. Theoretical analysis establishes the fundamental rate-distortion-reuse tradeoff and proves that soft retrieval reduces unnecessary transmissions compared to hard quantization under bounded semantic drift. Extensive simulations over diverse video scenarios demonstrate that the proposed MHN-based approach achieves substantial bit reductions around 14% on average and up to 70% in scenarios with gradual content changes compared to baseline.