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This is an unusual event. I've seen email apps that only delete the email from the phone but none that seem to delete the item only to have it reappear. In the meantime there are a couple of answers that might help us help you.
What device do you have?
What app are you using for email?
If you delete the item again does it stay gone? If not how many times do you have attempt to delete it before it doesn't come back?
Does it matter if you're on WiFi or data?
Is there anything you have tried? What is your method for deleting emails under these conditions?
In the meantime you might try clearing the app cache. Which reminds me, how long has this been happening on this device? Rereading your post it almost sounds like you just bought this device and right out of the box you are having this issue. Anyway, I would start by clearing the app cache. See if that clears it up. If not try clearing the app data. This will cause you to have to set the app up again but a fresh start could be what is needed.
Let us know what you find.
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