After spending time in the "help forums", I found the fix. But it was not to any help of the tech people from Blogger, it was a user named Cavebear. The "update" posted in the forum does not actually do anything to fix the situation.
OK. Go to settings on the left panel on blogger.com. Click "Settings". Click "Posts, comments and sharing". There is a box with your email address in it. Delete the email address and click "Save Settings". Now type your email into the box again and click "Save Settings".
You will now get an email at the address you entered and it will ask if you wish to subscribe to receiving notifications for comments being posted. Click "Subscribe". After this you will receive comment notifications once again. They look a little different than they used to look, but they are there at least.