There is a known issue when customers are unable to post comments through the community.

Here is the link to the official salesforce know issues list https://success.salesforce.com/issues_view?id=a1p3A0000001C9OQAU

While the workaround mentioned does address the issue, it should be noted that any email templates associated should be taken care. Make sure you check these areas and move all associated email templates into a public folder.

• Workflow rules and workflow email alerts.
• Process builder and associated email alerts.
• Email templates specified under support settings (Image below)