Audio-visual Target Speaker Extraction (AV-TSE) aims to isolate a target speaker's voice from multi-speaker environments by leveraging visual cues as guidance. However, the performance of AV-TSE systems heavily relies on the quality of these visual cues. In extreme scenarios where visual cues are missing or severely degraded, the system may fail to accurately extract the target speaker. In contrast, humans can maintain attention on a target speaker even in the absence of explicit auxiliary information. Motivated by such human cognitive ability, we propose a novel framework called MeMo, which incorporates two adaptive memory banks to store attention-related information. MeMo is specifically designed for real-time scenarios: once initial attention is established, the system maintains attentional momentum over time, even when visual cues become unavailable. We conduct comprehensive experiments to verify the effectiveness of MeMo. Experimental results demonstrate that our proposed framework achieves SI-SNR improvements of at least 2 dB over the corresponding baseline.