Audio-visual Target Speaker Extraction (AV-TSE) aims to isolate the speech of a specific target speaker from an audio mixture using time-synchronized visual cues. In real-world scenarios, visual cues are not always available due to various impairments, which undermines the stability of AV-TSE. Despite this challenge, humans can maintain attentional momentum over time, even when the target speaker is not visible. In this paper, we introduce the Momentum Multi-modal target Speaker Extraction (MoMuSE), which retains a speaker identity momentum in memory, enabling the model to continuously track the target speaker. Designed for real-time inference, MoMuSE extracts the current speech window with guidance from both visual cues and dynamically updated speaker momentum. Experimental results demonstrate that MoMuSE exhibits significant improvement, particularly in scenarios with severe impairment of visual cues.