Apparently the webmail has been broken for awhile. You should be receiving the emails, but webmail cannot display them.
Work around:
cPanel --> File Manager
Up one level above public_html ( /home/YourcPanelUserName )
Open Mail directory
Open directory for the email account you want
Open directory new
The emails should be oldest --> newest
Open in Editor or download a copy to your computer
This includes all the headers and routing information. But you should be able to find the Subject, From, and Content.