To address the problem that chip range walk exceeds half a chip period due to large Doppler shifts and long-time integration in high-dynamic scenarios, which degrades coherent integration gain and detection performance, this paper proposes a long-time coherent integration acquisition technology for weak DS/FH (Direct Sequence/Frequency Hopping) TT&C (Telemetry, Tracking, and Command) signals of spacecraft. Based on the traditional half-chip sliding cross-correlation matrix, a sliding-window matrix to be corrected is constructed first. Then, an extraction matrix is designed using 0/1 logic operations, and the sliding cross-correlation correction matrix is obtained by extracting from the sliding-window matrix to be corrected. Subsequently, chip range walk correction is completed by combining fractional delay compensation. Notably, the proposed technology maintains a computational complexity comparable to that of existing fast coherent integration acquisition technologies, while significantly improving frequency hopping coherent integration gain and detection performance. Verified by comprehensive simulation analyses under various conditions, the proposed method can effectively resolve the bottlenecks of coherent integration gain and detection performance in high-dynamic, large Doppler, and long-time integration scenarios. It not only provides a reliable technical solution for capturing weak DS/FH TT&C signals but also offers important theoretical guidance and practical value for the engineering implementation of related spacecraft telemetry and tracking systems.