Some mail servers will automatically delete suspected spam (sometimes without notice). Mail sent by web servers tends to be immediately suspect unless all anti-spam data (SPF, DKIM, etc.) indicates otherwise. Did you check you mail client’s spam folder for the missing message? If it’s there, your mail client may need to be configured to not spam such messages.
How did you configure the From: address in order notification settings? If the From: address’ domain does not match the domain name of the server, the message is more likely to be seen as spam. If it does not match, try using an address that does match. If it already matches, the anti-spam data included with the message might be inaccurate or missing. Your host will need to help you to get the correct mail server anti-spam data included in messages.
If all else fails, you may need to use an alternative SMTP service to have messages reliably get through. There are several alternative SMTP plugins available.