Apple does not allow 3rd party applications in the iOS App Store to interact in such a way with the default Mail application to make such a feature possible. 3rd party applications run in a sandboxed environment and are strictly prohibited any access to your mails.
On the other hand, Apple also does not allow 3rd party mail clients in the App Store, which theoretically could implement such a feature, but will never be accepted after the App review process (unless Apple would choose to change that policy in the future).
You could circumvent these limitations by jailbreaking your iPhone. However, even then it is very unlikely you'll find a ready-made solution which works exactly as you described it. You'd probably have to develop such an app yourself, and then install it on your jail-broken iPhone.
If you don't want to jailbreak, nor go through the trouble of actually developing such an app yourself, I suggest you go for a different approach. You could for example keep resending the notification by the server until you confirm reception at the server-side.
I also suggest sending an SMS through an SMS gateway instead of an e-mail. This has the added benefit you can configure a custom tone (and a more attention grabbing one if you will), just for that specific contact number. Also SMS notifications can be configured to repeat every 2 minutes for up to 10 times, so you would only need to resend the SMS every 20 minutes. Finally, this would also work when you don't have a data connection available (for example when roaming), and in case you don't have a push mail account it should reach you faster than an e-mail too.
You could also do both SMS and email for yet another fail-safe. I'll leave it up to you on how critical these notifications actually are!