Generally speaking, if emails of other types are being received from the store, but it appears only that the "admin" is not receiving emails, then there remains pretty much two things to verify.
1) that the emails for admin related notification are being generated, and 2) that the recipient email account can otherwise receive emails (not a full email account for example or the email being otherwise marked as spam). If an account is created that uses the same email address then would want to see if none, one, or two emails get received for say a purchase.
The following FAQ goes into the email issue troubleshooting and correction:
https://www.zen-cart.com/content.php...ved-or-sending
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