|In this situation you will need to use the Case Comments Publisher component on your case Detail Pages for your Community Users to add new comments. If you are making edits to your Case Detail Page in the Community Builder and you do not see this component, then you are more than likely using the Record Detail Page Variation versus either the Basic Case Detail or the Chatter Case Detail Variation. Please see the following for comparison:
To switch the Page Variation for your Case Details pages you will need to access the Page Manager from the navigation on the left in the Community Builder and then Select "Case" under Salesforce Object Pages. From here you can change the Active Page. Please see the following:
|Case Detail Components using Record Detail Variation:||Case Detail Components using Chatter Case Detail Variation:|
Once the Case Specific components become available you can then add the Case Comments and Case Comments Publisher to the page. Once published your users will then be able to add comments on the Case Record.