On Cpanel’s Tweak Settings you can limit the maximum each domain can send out per hour. The problem is that this limit also applies to Mailman mailing list hence causing problem for mailing list owners.
The problem happen when the mailing list has members more than the maximum number of email a domain can send per hour. Once the mailing list hit the max limit, the emails start to be bounced back or dropped by Exim from its queue.
To fix this problem administrator can set a limit for a specific domain on the server by modifying /var/cpanel/maxemails file and add the domain that want its limit to be override:
Then run /scripts/build_maxemails_config to apply the new limit.