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It is possible that the iPhone has lost connected with email server. First we can reset your iPhone and see if it works or not. Press and hold down the Power button and Home button at the same time until it shows the Apple logo. When you see the Apple logo, release the buttons and let it boot.
Note : Power button is the button you use to turn off your iPhone or its screen. Home button is the round button at front bottom.
Check Mail. If that didn't work, then go to Settings > Mail, Contacts, Calendars. Tap your Gmail account, tap Delete account. Then tap Add Account and tap Gmail and add your account. This will re-establish the connection.
Please let me know if that didn't work, so we can continue troubleshooting