- Tail /var/log/cron.log and see "Authentication token is no longer valid; new one required".
- Run "chage -l root" to check the aging information of root account, and "password must be changed" message shown up.
- Generate a new password from https://strongpasswordgenerator.com, then run passwd command to change to the new passwd for root.
- Check /var/log/cron.log again after a cron job is executed, and the cron.log seems OK. The problem fixed.
Conclusion: Since the cron job is essential for automatic log rotation. If cron job has any problem, the log files don't get rotated even manual run has no problem at all.