If you have trouble getting email on your mobile device and you have checked the settings, it may be related to CAPTCHA.
1. Quit all email applications and logout Google email if necessary on ALL your devices.
2. On the iOS device your having issues with, click or enter this address in Safari: http://www.google.com/accounts/DisplayUnlockCaptcha
3. Login with your full email address and password when prompted, then type the characters for the image you see (if required) and Continue. (See below)
4. You should now be presented with “Account Access Enabled”, at this point, launch the email application on your iOS device and check for new mail. If this does not resolve the issue then there may be something else preventing your mail application from connecting. (See Below)