Magento doesn't rotate logs like you seem to be implying. However, you've likely seen logs get rotated on some servers in locations like
/var/log/ where those are rotated by the OS itself. On many Linux servers you'll find a folder called
/etc/logrotate.d/ that contains definitions of what files/logs you'd like to rotate. Here's an example one I use to rotate logs for Magento.
su www-data www-data
create 640 www-data www-data
This runs logrotate each night, compressing and renaming log files to only keep single day increments of the logs up to 50 days. The username
www-data should be substituted for whichever user your webserver is running as.
Some more info on using logrotate: