I think there is some issue with the Gmail configuration as Exchange mail on iPhone

According to Google blog Google has shutdown on all the new mobile devices.

If you have configured your Gmail account using Google Sync (exchange) and is working fine then its because you had been using it (configured it) on your mobile device before they shutdown their services.

Gmail Exchange now doesnt work on your new iphone as explained here

The way around:
Configure your Gmail as IMAP account.
Make sure IMAP is enabled for your Gmail account

Tap Settings on the iPhone Home screen.
Go to Mail, Contacts, Calendars.
Tap Add Account under Accounts.
Choose GMAIL
Enter your name under Name.
Type your full Gmail address under Address.
Enter your Gmail password under Password.
Type “Gmail” under Description (or leave it set to the default, “Google Mail”).
Tap Next.
Make sure ON is selected for Mail.
Tap Save.
Press the Home button.

And you’ll start to see your Gmail working in iOS Mail.

Sync Google Contacts
Settings > Mail, Contact, Calendars … > Add account … > Other > Add CardDAV account

Enter google.com as server and then your Gmail login credentials.

Save settings and goto Contacts. Click Groups on the top left and select All Google under Google. Then click the refresh button on the top left.

Thats it : ) in a few seconds all your Google contacts will show up.

This is a quick and I will update this post with screenshots soon.