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TCP performance is adversely affected by frequent route failures due to mobility in mobile ad hoc networks. Most of the recent attempts to improve TCP performance focused on transport layer mechanisms and several modifications to TCP were proposed to prevent it from invoking congestion control for packet losses caused by route failures. We present a new approach to improve TCP performance at the network layer: reducing route failures by making route caches in on-demand routing protocols adapt to topology changes quickly and efficiently. The route cache in on-demand routing protocols is used for routing decisions, however, due to frequent topology changes, cached routes easily become stale, seriously degrading TCP throughput. In our prior work, we proposed a distributed adaptive cache update algorithm to address the cache staleness issue in the dynamic source routing protocol (DSR), an important on-demand routing protocol. In this paper, we investigate the impact of this algorithm on TCP performance, without any modification to TCP. We show through detailed simulations that this algorithm significantly improves TCP throughput and reduces normalized routing overhead. We conclude that it is important to make route caches reflect topology changes quickly so that the effect of mobility on TCP is reduced.