The Mailman system is written in Python and although rare, is sometimes susceptible to corruption. If Mailman can't start and you cannot find another reason for this, it may be that some of the configuration files are corrupted. In that case, it's best to simply reinstall the Mailman RPM.
To reinstall Mailman, you would run the following two commands:
rpm -e --nodeps cpanel-mailman
/usr/local/cpanel/scripts/check_cpanel_rpms --fix --targets=mailman
This will remove the cpanel-mailman RPM and then reinstall it.