An incremental relaying protocol is a promising scheme for preventing the inefficient use of resources in half-duplex cooperative relay networks. In particular, the incremental selection amplify-and-forward (ISAF) relaying scheme is a well-designed protocol under the condition that the source-to-destination (SD) link is static during the two transmission phases. However, from a practical viewpoint, the SD link is not static but varies with time, and thus the ISAF relaying scheme may not work well in the field. In this work, we first show that the outage performance of the ISAF relaying scheme may decrease when the SD link is not static during the two transmission phases. We then propose a modified version of the ISAF relaying scheme which overcomes such a limitation of the ISAF relaying scheme under time-varying environments. Finally, numerical and simulation results are provided to support our findings.