The speaker extraction algorithm extracts the target speech from a mixture speech containing interference speech and background noise. The extraction process sometimes over-suppresses the extracted target speech, which not only creates artifacts during listening but also harms the performance of downstream automatic speech recognition algorithms. We propose a hybrid continuity loss function for time-domain speaker extraction algorithms to settle the over-suppression problem. On top of the waveform-level loss used for superior signal quality, i.e., SI-SDR, we introduce a multi-resolution delta spectrum loss in the frequency-domain, to ensure the continuity of an extracted speech signal, thus alleviating the over-suppression. We examine the hybrid continuity loss function using a time-domain audio-visual speaker extraction algorithm on the YouTube LRS2-BBC dataset. Experimental results show that the proposed loss function reduces the over-suppression and improves the word error rate of speech recognition on both clean and noisy two-speakers mixtures, without harming the reconstructed speech quality.