This post is a steemjs example of how to find out the number of times an author(user) comments on a post.
Step 1:
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.
Step 2:
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