Substrate logs to stderr and stdout. It is impossible to organize log rotation without copying previously logged data. E.g. logrotate has to be configured with copytruncate option that copies the file and truncates it, losing some data in the process.

Would be best to use a logger that supports rotation out of the box, or at least allows reopening output file on SIGHUP
https://github.com/emabee/flexi_logger looks promising, as long as there's no performance regression.