If the e-mail address you've entered is correct, check to make sure that you have message boards enabled and that you have selected the checkbox labeled "Get message board replies" (https://www.insanejournal.com/support/faqbrowse.bml?faqid=108). Save your settings and see if this corrects the problem. If you've chosen to receive HTML e-mails, and are still not getting any notifications, try turning this option off.
If the above solution doesn't work, and you haven't exceeded your e-mail account size allocation, then it is very likely the problem is on your receiving mail server's end. Check the spam and junk mail filters on your e-mail account. Adjust them to allow for e-mail from email@example.com . If everything is in working order with your account, check with your ISP/mail provider and tell them that you're not getting e-mail.
Many providers are not aware of their mail filters. The most popular mail transport package, "sendmail", comes with mail filters enabled by default that appear to block some InsaneJournal comment e-mail. You should let your provider know that you are not receiving e-mail, and ask that they adjust their sendmail filters.