Or you could change your log rotation system altogether, and use logrotate if your OS has it.
The general idea is : you dom't use rotatelogs, you write the logs normally to a file.
With cron, you regularly run logrotate, as often as you want.
It has a configuration file that tells it which files to rotate, how often, in function of which criteria, what to do before and after the rotation, how many "back-copies" to keep before starting to overwrite them etc.. It does this cleanly and without necessarily interrupting the process whose files it is rotating.
"man logrotate" under Linux is pretty explicit.