Você deve usar a diretiva copytruncate em sua configuração logrotate para este arquivo de log.
copytruncate Truncate the original log file in place after creating a copy, instead of moving the old log file and optionally creating a new one. It can be used when some program cannot be told to close its logfile and thus might continue writing (appending) to the previous log file forever. Note that there is a very small time slice between copying the file and truncating it, so some logging data might be lost. When this option is used, the create option will have no effect, as the old log file stays in place