This article from gigaom explains the problem and offers some "workarounds" (Not really workarounds if you're set on using exchange). https://gigaom.com/2013/07/05/push-alternatives-for-your-gmail-messages-on-ios/
So anyone upgrading from their older iPhone 4S to a iPhone 5s, 6, or 6 Plus (and iPads after iPad 3 or 4) you will lose your ability to use MS Exchange Server sync with your free gmail accounts. I found out the hard way that you will also lose it on an older device if you setup 2-step verification on your gmail account. I read some reports that Palm WebOS phones still work with the Exchange Server and Gmail, but that maybe because WebOS is open sourced now, somGoogle may not have a choice.
Let's be clear this is a Google / Gmail change, they discontinued another service because people weren't using the Gmail app on the iphone, however they said they did it because it wasn't secure. I have a google apps account for a business and exchange still works for that account, So they must want people to either pay for an Email account or switch to Android. The company I work for uses the native. iOS Mail app with Lotus Notes, and will be soon with MS Outlook, and Microsoft has no problems with Office 365 via Exchange to an iOS device.
if you hav multiple email addresses and moving all of them to custom domains and google apps isn't an option, you might want to try creating one Google Apps account then creating alias domains to create other email addresses all accessible via Exchange and the iOS Mail app, (i.e. user@primarydomain.com; user2@sub1.primarydomain.com; userX@subx.primarydomain.com) Google still allows you to do this. I've heard you can have up to 10 alias domains.