Do you mean that if a user sends a email with a comment for a closed issue, the comment is actually added but you do not receive notifications? Because usually there is a status property in workflows which forbids editing issue while in the closed status. In this case a comment will be not added to the issue and you will not receive a notification.
If you use Jira Service Desk then there are two notifications: for customers and agents. If you do not have Jira Service Desk then you provide all settings for notifications in the project notification scheme. There is not way to restrict notifications by status. Have a look at the project notification scheme. What is there for Issue Commented event?
You can read more about notification schemes here
Then Reporter, All watchers and Assignee must get notifications even on closed issues. I searched the internet I found similair problems to yours but there were no solutions.
I would offer you to enable outgoing email logging and have a look at the logs. Also try to follow the KB below
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