This post is a steemjs example of how to find out the number of times an author(user) comments on a post.
Enter the author for the post(defaulted to greenman in this case). Click the button "Get Author Posts".
This will populate the post links drop-down with the last 50 posts for that author.
Select the post from the drop for which you want to see the author comments count data. "Click the Get Comments Data".
This will populate the data in a table sorted by count in descending order.
The test URL can be found at https://rawgit.com/hackerwhacker/SteemJS/master/AuthorComments.html
The source code can be found on github at https://github.com/hackerwhacker/SteemJS/blob/master/AuthorComments.html