The built-in behavior of WP is to notify the author of the post upon receiving new comments. However for me, it only seems to be working for certain posts. I found this odd as posts that were published yesterday are not sending out notifications yet a test post I created today is sending them out no problem.
I have no idea where to start looking for a solution as the both the authors email address and the address under General -> Settings are both valid.
Thanks in advance for any help.